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## Identify both the x- and y-intercepts of the linear equation graphed on the coordinate plane above. Use the intercepts to write an equation of the line in point-slope form, slope-intercept form, and general form of a linear equation.Complete your work in the space provided or upload a file that can display math symbols if your work requires it. In your work, be sure to include the coordinates for both intercepts and the equations of the line in all three formats.

The x int (where the line crosses the x axis) is (-2,0)
the y int (where the line crosses the y axis) is (0,-2)

(-2,0)(0,-2)
slope = (-2 – 0) / (0 – (-2) = -2/2 = -1

y = mx + b
slope(m) = -1
use either of ur points (-2,0)…x = -2 and y = 0
sub and find b
0 = -1(-2) + b
0 = 2 + b
-2 = b

so ur equation in slope intercept form is : y = -x – 2

y = -x – 2
x + y = -2
x + y + 2 = 0 <== general form

there can be 2 answer for point slope form…
y – y1 = m(x – x1)
slope(m) = -1
(-2,0)…x1 = -2 and y1 = 0
sub
y – 0 = – (x – (-2)
y – 0 = -(x + 2) <=== point slope form

y – y1 = m(x – x1)
slope(m) = -1
(0,-2)…x1 = 0 and y1 = -2
sub
y – (-2) = – (x – 0)
y + 2 = – (x – 0) <== point slope form

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## Which equation represents a linear function? Equation 1: y = 2×2 + 1 Equation 2: y = 8x + 1 Equation 3: y = 5×3 – 1 Equation 4: y2 = 4x – 1 A. Equation 1 B. Equation 2 C. Equation 3 D. Equation 4

Which equation represents a linear function? Equation 1: y = 2×2 + 1 Equation 2: y = 8x + 1 Equation 3: y = 5×3 – 1 Equation 4: y2 = 4x – 1 A. Equation 1 B. Equation 2 C. Equation 3 D. Equation 4

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## The flip flop a lot company makes and sells flip flops they have one linear function that represents the cost of producing flip-flops and another linear function that models how much income they get from those flip-flops describe the key features that will determine if these linear functions ever intercepted

If the linear functions have the same slope but different y-intercepts, they will never intercept. If the If the linear functions have the same slope and the same y-intercet, they are the same line. If the linear functions have different slopes and different y-intercepts, they will intercept.

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## How many solutions does a system of two linear equations have if the slope of each equation is different and the y-intercepts are the same?

How many solutions does a system of two linear equations have if the slope of each equation is different and the y-intercepts are the same?

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## Determine whether the function is linear or quadratic. identify the quadratic, linear, and constant terms y= (x-5)(5x+4)-5x^2

Linear means that it is 1st degree, means it has x¹ basically the highest number is 1 for the power of the placeholder

quadratic means it is 2nd degree, means it has x² in it

so expand and simlfiy
(x-5)(5x+4)-5x²=
5x²-21x-20-5x=
-21x-20

so y=-21x¹-20
it’s linear because the squared terms cancel each other out

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## If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour

If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour

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## If a wheel with a radius of 30 inches spins at a rate of 500 revolutions per minute, find the approximate linear velocity in miles per hour.

30 inches @ 500 rpm = 15,000 inches per minute

15,000 inches per minute = 900,000 inches per hour (multiply by 60)

1 mile = 5,280 feet (google-able fact you shouldn’t have to memorize)
1 foot = 12 inches (you probably already know this)
900,000 inches = 75,000 feet (divide by 12)

75,000 feet = 14.20454545454545. . . miles (divide by 5280)

Linear velocity in miles per hour is 14.20454545454545. . . miles per hour.

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## Which statement correctly describes the slope of the linear function that is represented by the data in the table? Table (It may move to the left a bit when it is actually posted, sorry. It shouldn’t be hard to read though) x y 8 -8 8 -4 8 0 8 4 8 8 a.The slope is positive. b.The slope is negative. c.The slope is zero. d.There is no slope.

Answer: d. There is no slope.

Step-by-step explanation:

We know that slope =

For the given table, since there is no change in x coordinate .

Thus the change in x coordinate is 0.

Therefore, slope=

which means the slope does not exist.

Hence, (d) is the right option. There is no slope.

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## In the table, x represents minutes, and y represents the altitude of an airplane. Table x y 15 22,500 20 20,000 25 17,500 30 15,000 Which statement is correct about the slope of the linear function that the table represents? a.The slope is positive because as the minutes decrease, the altitude increases. b.The slope is positive because as the minutes increase, the altitude increases. c.The slope is negative because as the minutes decrease, the altitude decreases. d.The slope is negative because as the minutes increase, the altitude decreases.

In the table, x represents minutes, and y represents the altitude of an airplane. Table x y 15 22,500 20 20,000 25 17,500 30 15,000 Which statement is correct about the slope of the linear function that the table represents? a.The slope is positive because as the minutes decrease, the altitude increases. b.The slope is positive because as the minutes increase, the altitude increases. c.The slope is negative because as the minutes decrease, the altitude decreases. d.The slope is negative because as the minutes increase, the altitude decreases.

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## SPENT 50 POINTS ON THIS QUESTION PLEASE HELP In the table, x represents minutes, and y represents the altitude of an airplane. Table x y 15 22,500 20 20,000 25 17,500 30 15,000 Which statement is correct about the slope of the linear function that the table represents? a.The slope is positive because as the minutes decrease, the altitude increases. b.The slope is positive because as the minutes increase, the altitude increases. c.The slope is negative because as the minutes decrease, the altitude decreases. d.The slope is negative because as the minutes increase, the altitude decreases.

Slope=changey/changex
well, the slope will be positive when the minutes (x) are increasing and the altitude (y) is also increasing
the slope will be negative when the minutes (x) are increasing and the altitude (y) is decreasing

we see that x increase
and y decreases
so the slope is negative because as minutes incrases, altitude decreases

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## Find a linear approximation of the function f(x)=sqrt[3]{1+x} at a=0, and use it to approximate the numbers sqrt[3]{.96} and sqrt[3]{1.02}

5 in 0.05 is 10 times greater than 5 in 0.005.

Step-by-step explanation:

To find : In which number does the digit 5 have greater value 0.05 or 0.005 how many times as great is it and how do you know ?

Solution :

According to the place value stem,

Ones      Tenths      Hundredths     Thousandths

0              0                   5                                           – 0.05

0              0                   0                        5                 – 0.005

In 0.05 5 is in hundredths place and in 0.005 5 is in thousandths place.

So, 5 in 0.05 is 10 times greater than 5 in 0.005.

As

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## Jillian’s begins to solve a linear equation that results in a variable expression set equal to the same variable as expression. Which is the best interpretation of this solution

Ur points are set up like this (x,y)….so ur x axis number, then ur y axis number…so 2 of the points that are on ur line are (0,12000) and (120,0)
u do not subtract 2000 by 4000…if u wanted to use those points, they would be (80,4000) and (100,2000)

slope (rate of change) = (y2 – y1) / (x2 – x1)
(0,12000) …x1 = 0 and y1 = 12000
(120,0) ……x2 = 120 and y2 = 0
slope = (0 – 12,000) / (120 – 0) = -12,000/120 = -100 <== ur slope

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## Which type of function is represented by the table of values below? x y 1 4 2 16 3 64 4 256 5 1,024 exponential linear quadratic square root

False

Step-by-step explanation:

Suposse that we are given a function f(x) and a constant value h.

1. Case:

If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.

2.Case:

If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.

3.Case:

If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.

4. Case:

If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.

For example:

If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.

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## How many solutions does this linear system have? one solution: (8, 0)one solution: (0, 8)no solutioninfinite number of solutions

How many solutions does this linear system have? one solution: (8, 0)one solution: (0, 8)no solutioninfinite number of solutions

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## Which of the following is a linear function? y = 3×2 y = 1 over 3x y = x3 + 5 2 over 3x = y − 1

Which of the following is a linear function? y = 3×2 y = 1 over 3x y = x3 + 5 2 over 3x = y − 1

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## Which of the following functions is not a linear function? A)f(x) = -2 B)f(x) = x – 2 C)f(x) = 2x D)f(x) = x 2

Which of the following functions is not a linear function? A)f(x) = -2 B)f(x) = x – 2 C)f(x) = 2x D)f(x) = x 2

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## If a wheel with a radius of 70 inches spins at a rate of 600 revolutions per minute, find the approximate linear velocity in miles per hour.

If a wheel with a radius of 70 inches spins at a rate of 600 revolutions per minute, find the approximate linear velocity in miles per hour.

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## Which linear inequality is represented by the graph?

The linear inequality that is represented by the graph is:

## Step-by-step explanation:

From the graph of the given function we see that the graph is a solid line passing through (0,3) and (-6,0) and the shading is towards the origin.

Hence, we will check each of the given options.

A)

We see that the line of this inequality is a line passing through (0,4) and (-2,0) and shading towards the origin.

Hence, option: A is incorrect.

C)

The graph of this inequality is a solid line passing through (0,3) and (-6,0) and the shading is away from the origin.

Hence, option: C is incorrect.

D)

The graph of this inequality is a solid line passing through the point (0,3) and (-3/2,0) and shading away from the origin.

Hence, option: D is incorrect.

B)

When we plot the graph of this inequality we see that it matches the given graph.

Hence, option: B is the correct answer.

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## Consider the system of linear equations 2x+3y=8 and 3x+y=-2.Which statement correct

Consider the system of linear equations 2x+3y=8 and 3x+y=-2.Which statement correct

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## Which systems of linear equations has the ordered pair(4,-5)as a solution? A)2x-5y=-30 and 7x+4y=-19 B)6x-y=-29 and 8x+3y=-17 C)3x-2y=22 and 2x+9y=-37 D)5x-6y=49 and x+8y=-27

So hmmm we’ll start off by using the decimal format for the percentage, thus 15% is just 15/100 or 0.15 and 7% is just 7/100 or 0.07 and so on

notice, the concentration of alcohol in the 15% is, well, 0.15 :), so for a quantity of whatever, it’d be 0.15whatever

anyway, for water… water has no alcohol whatsoever, so the concentration is 0%, or 0/100 which is 0.00 or a flat 0

we know that we’ll be adding “x” water with the 14mL to get “y”, thus 14+x = y

and the concentrated quantities will also add up to -> 14(0.15) = 2.1, thus
2.1 + 0x = 0.07y

solve for “x”.

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## Marissa researched the cost to have custom T-shirts printed by several local and online vendors. She found that each store’s charge for the job could be modeled by a linear function that combined a flat charge for artwork with a per T-shirt rate. Marissa plotted the functions on a coordinate grid and found that two of the functions produced lines that had the same y-intercept. How should Marissa interpret this result? A:Those two vendors charge the same rate per shirt. B:Those two vendors charge the same flat rate for artwork. C:Those two vendors will have the same total cost to produce one shirt. D:Those two vendors will charge the same total cost for any size job.

C. Yes, because the population values appear to be normally distributed.

Step-by-step explanation:

Given is a graph which shows the distribution of values of a population

The graph has the following characteristics

i) Bell shaped

ii) symmerical about mid vertical line

iii) Unimodal with mode = median =mean

iv) As x deviates more from the mean probability is decreasing and also curve approaches asymptotically the x axis

Hence we find that the curve is a distribution of normal

Option C is right

C. Yes, because the population values appear to be normally distributed.

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## Which of the following describes the graph of a linear function? It is V shaped and passes through the origin. Its y-values increase at a constant rate as its x-value increases. It is a straight line in one portion and a curve in another portion. Its y-values increase at a nonconstant rate as its x-value increases.

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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## Create a linear equation to represent the monthly bill. When will the plans cost the same? Explain which plan is a better option. Plan A \$25.75 plus \$.75 per min Plan B \$20.99 plus 1.00 per min

Create a linear equation to represent the monthly bill. When will the plans cost the same? Explain which plan is a better option. Plan A \$25.75 plus \$.75 per min Plan B \$20.99 plus 1.00 per min

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## You are considering two activity packages while on vacation. One cost \$192 and includes 3 hours of horse back riding on the beach and 2 hours of jet ski rental. The second cost \$213 and includes 2 hours of horse back riding on the beach and 3 hours of jet ski rental. Select the system of linear equations that represents this scenario. Let h = cost of one hour of horseback riding and let j = cost of renting jet ski for one hour. (Answers below)

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.