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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.

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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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Rewrite the slope-intercept form equation into standard form. y = –2x + 4 A. x + 2y = 4 B. 2x + y = 4 C. 4x + y = 2 D. 4x + 2y = 0 Please select the best answer from the choices provided

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The answer is B because if you have y = -2x + 4, to get the -2x to the same side as y, you need to add, making it y + 2x = 4. It would also be postive no matter what because this formula needs to be positive. … and the standard form is Ax + By = C.. Making your final answer 2x + y = 4.

Hope This Helps!
Correct Me If I’m wrong!

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Given the system of inequalities: 4x – 5y < 1 y – x < 3 Which shows the given inequalities in slope-intercept form?

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Given the system of inequalities: 4x – 5y < 1 y – x < 3 Which shows the given inequalities in slope-intercept form?

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What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5x + 10 and passes through the point (15, –5)? The equation of the line in slope-intercept form is y =-5/3 x + ____

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What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5x + 10 and passes through the point (15, –5)? The equation of the line in slope-intercept form is y =-5/3 x + ____

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\\\——-!!!!!40 POINTS!!!!—–\\\\The graph below shows the relationship between the number of months different students practiced tennis and the number of matches they won: Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points) Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)

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Answer:

3 hours.          

Step-by-step explanation:

Let x be the time taken by shoe repairman to repair one pair.

We have been given that his assistant, who takes twice as long to repair a pair of shoes. So time taken by his assistant to repair one pair of shoes would be 2x.

The number of pair of shoes repaired by repairman in one hour would be frac{1}{x}.

The number of pair of shoes repaired by assistant in one hour would be frac{1}{2x}.

We have been given that together they can fix 16 pairs of shoes in an eight-hour day. We can represent this information in an equation as:

frac{1}{x}+frac{1}{2x}=frac{8}{16}

frac{1}{x}+frac{1}{2x}=frac{1}{2}

Let us have a common denominator.

frac{2*1}{2*x}+frac{1}{2x}=frac{1}{2}

frac{2}{2x}+frac{1}{2x}=frac{1}{2}

frac{2+1}{2x}=frac{1}{2}

frac{3}{2x}=frac{1}{2}  

Upon cross multiplying our equation we will get,

2x*1=3*2

2x=3*2

frac{2x}{2}=frac{3*2}{2}

x=3

Therefore, it take 3 hours for the repairman to fix one pair of shoes by himself.

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Write an equation of the line in slope-intercept form that crosses the y-axis at 3 and increases at a rate of 1?

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It is very much more instructive if you can visualize the images of triangles PQR, P’Q’R’ and P”Q”R”.  You can plot this on square paper, or on any technology tool.

On the graph, you can join lines PP’, QQ’ and RR’ to confirm that they meet at the origin O(0,0), which is also the centre of dilation.

Part A
Next, you can compare the lengths OP’ and OP using the distance formula, namely mOP’=sqrt(1^2+2^2)=sqrt(5), while mOP = sqrt(3^2+6^2) = sqrt(45) = sqrt(3^2 *5) = 3sqrt(5).

This demonstrate that the scale factor of dilation, equal to mOP’/mOP equals sqrt(5)/3sqrt(5)=1/3.

Try the same with OQ’ and OQ, as well as OR’ and OR.  You should get the same factor of 1/3.  If not, there is an error in some of the calculations.

Part B: 
Points reflected about the y-axis goes through the transformation as follows:
Sy (x,y) -> (-x,y)
That means you only have to flip the sign of x-coordinate.
For example, P(3,-6) will have its reflection on P”(-3,-6), and so on.

Part C:
PQR and P”Q”R” are congruent because all simple reflections reflected about any line or point conserve the lengths and angles of shapes.

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Rewrite the linear function 1/2x-3y=16 in slope-intercept form.

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A function will not have any repeating x values…it can have repeating y values, just not the x ones.

The inverse of each of these points can be found by switching the x values and the y values.

( -4,3) , (-2,7) , (-1,0) , (4,-3), (11,-7) } this is a function because it has no repeating x values.

its inverse : (3,-4) , (7,-2), (0,-1) , (-3,4) , (-7,11)…..and this is also a function…no repeating x values

so ur answer is the first answer choice

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Rewrite the linear function 6x+2y=10 in slope-intercept form.

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A function will not have any repeating x values…it can have repeating y values, just not the x ones.

The inverse of each of these points can be found by switching the x values and the y values.

( -4,3) , (-2,7) , (-1,0) , (4,-3), (11,-7) } this is a function because it has no repeating x values.

its inverse : (3,-4) , (7,-2), (0,-1) , (-3,4) , (-7,11)…..and this is also a function…no repeating x values

so ur answer is the first answer choice

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The equation of line MN is y=3/4x+5 In slope-intercept form, write the equation of the line that is perpendicular to MN and that passes through the point (–6, –2).

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Answer:

The probability that he chooses 2 oranges is:

                dfrac{5}{14}

Step-by-step explanation:

The odds of choosing a orange from a basket is:

                           dfrac{5}{3}

If  O denote orange

and T denote the total number of fruits

Then the odds of selecting an orange is given by:

 dfrac{O}{T-0}=dfrac{5}{3}

This means that:

The total number of fruits in basket i.e. T=8

so that the ratio matches.

Hence, the probability of getting orange in first draw= 5/8

Now , the second draw is independent of first and the fruits are not replaced.

This means now we have to choose fruits from remaining 7 fruits in the basket .

Probability of getting orange in second draw is: 4/7

Hence, the probability of choosing 2 oranges if the fruits are not replaced is:

  =dfrac{5}{8}times dfrac{4}{7}\\\=dfrac{5}{14}

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Write an equation in​ point-slope form of the line that passes through the given​ points, then write the equation in​ slope-intercept form. ​(−9​,7​), ​(9,11) What is the​ point-slope form of the equation of the​ line?

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Answer:

width of the rectangular prism is 4.5 inches.

Step-by-step explanation:

Carltren solves for w and writes the equivalent equation as w=frac{V}{lh}

Now, we have to find the width of a rectangular prism that has a volume of 138.24 cubic inches a height of 9.6 inches and a length of 3.2 inches.

Thus, we have

V = 138.24 cubic inches

l = 3.2 inches

h = 9.6 inches.

Substituting these values in the above formula to find w

w=frac{138.24}{3.2cdot9.6}

On simplifying, we get

w=4.5

Thus, width of the rectangular prism is 4.5 inches.

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Write an equation in​ slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. ​(−8​,−8​); y=−3x+5 Write an equation for the line in​ slope-intercept form.

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The statement ” varies directly as ,” means that when increases,increases by the same factor. In other words, and always have the same ratio:

 = k   
where is the constant of variation.
We can also express the relationship between and as:
y = kx   
where is the constant of variation.

Since is constant (the same for every point), we can find when given any point by dividing the y-coordinate by the x-coordinate. For example, if varies directly as , and y = 6 when x = 2 , the constant of variation is k =  = 3 . Thus, the equation describing this direct variation is y = 3x .

Example 1: If varies directly as , and x = 12 when y = 9 , what is the equation that describes this direct variation?

k =  =  
y =  x

Example 2: If varies directly as , and the constant of variation is k =  , what is when x = 9 ?

y =  x = (9) = 15

As previously stated, is constant for every point; i.e., the ratio between the -coordinate of a point and the -coordinate of a point is constant. Thus, given any two points (x 1, y 1) and (x 2, y 2) that satisfy the equation,  = k and  = k . Consequently,  =  for any two points that satisfy the equation.

Example 3: If varies directly as , and y = 15 when x = 10 , then what is when x = 6 ?

 =  
 =  
6() = y 
y = 9

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Write the equation of the line perpendicular to 3x + y = -8 that passes through (-3,1) . Write your answer in slope-intercept form. Show your work.

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Looks as tho’ there are several possible answers, which you unfortunately have not shared.  But anyway…    We can rewrite   y=3/4x−5/2y    in standard form with confidence.  Standard form here would be   y = mx + b (slope-intercept form).

In   

y=3/4x−5/2y   there are 2 terms in y.  We need to combine them.
To do this, add (5/2)y to both sides.  This results in:

y + (5/2)y = (3/4)x

Can you combine the coefficients of y into one fraction?  1 + (5/2) = ?

Result:  (7/2)y = (3/4)x.  Multiply both sides of this equation by (2/7) to solve the equation for y.

Note that there is another “standard form” for this equation; it looks like either Ax+By+C=0 or Ax+By=D.  Can you put  

(7/2)y = (3/4)x  into one of these forms?

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Write an equation in slope-intercept form

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Answer:

y= x -6

Step-by-step explanation:

y=mx + b

Since this line is // to the one with a slope = 1, that means m = 1, hence 

y=x + b. Now let’s calculate b. The graph passes by A(1,-5), you replace x and y by their related coordinates:

-5 = 1 + b → →b = -6

Final linear equation ; y = x -6

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