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Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3? y + 2 =(x + 3) y – 2 = (x – 3) y + 3 = (x + 2) y – 3 = (x – 2)

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# Tag: pointslope

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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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What is the equation in point−slope form of the line passing through (−2, −5) and (2, 3)?

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**Answer:**

(A)

**Step-by-step explanation:**

It is given that lines v and w are parallel, then from the given figure, ∠2 and ∠6 form corresponding angle pair, therefore ∠2=∠6.

A.**∠2+∠6=180°, his is incorrect** because ∠2 and ∠6 form corresponding angle pair and are equal.

B.**∠5≅∠8** because ∠5 and ∠8 form vertically opposite angle pair. Thus, this option is **correct.**

C.Since, sum of interior angles on the same side of transversal is 180°, therefore **∠3+∠5=180°, thus this option is correct.**

D.**∠1≅∠5 **because ∠1 and ∠5 form the corresponding angle pair and are equal. Thus, this option is **correct.**

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What is the equation in point-slope form of the line passing through (1, 9) and (−1, 11)?

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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

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**

**On simplifying, we get**

**Thus, width of the rectangular prism is 4.5 inches.**

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4x – 8y = 8 — subtract 4x

-8y = 8 – 4x — divide by -8

y = -1 + (1/2)x — reorder to match “mx + b”

y = (1/2)x – 1

in y = mx + b, “m” is the slope and “b” is the y-intercept. so for part B, your slope is (1/2) and your y-intercept is (-1). take the sign with you.

for part C, you’ll need to know point-slope form: (y – y1) = m(x – x1)

you’ll also need to be aware that “perpendicular” lines have a slope that is the opposite reciprocal of the original line.

the original slope is (1/2). change the sign to negative and form a reciprocal: your new slope is -2. plug that into your point-slope form

(y – y1) = m(x – x1)

(y – y1) = (-2)(x – x1)

and lastly, plug in your given point: (1, 2)

y – 2 = (-2)(x – 1)

so, just to look a little neater without all of the work:

A) y = (1/2)x – 1

B) m = (1/2), b = -1

C) y – 2 = (-2)(x – 1)

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Given that the line is parallel to y = -4 is the first clue. The line y = -4 is a horizontal line. All horizontal lines have a zero slope.Since your equation is parallel to that it must have the exact same slope. So you will use m = 0.Then plug in the (3,3) for the x and y in the slope intercept form of an equation and solve for b.y = mx +b3 =0 (3) + b3 = 0 + b3 = bSo to write the equation required for this question substitute the 3 in for the b and the zero in for the m (slope) and simplify.y = mx + by = 0x + 3y = 3 The answers from Katherine and Michael were the best method for solving. This is just another way to do the problem if you are not familiar with point slope form. 7/20/2013 | Bethanie F. CommentKatherine P.Saint Paul, MN0 0This problem provides you with a point (3,3) and a slope (parallel to y = -4, which is a slope of zero).Let’s save you some time by using point slope form to write your equation.y – y1 = m(x – x1)y – 3 = 0(x – 3)y – 3 = 0y = 3 <– the equation for your line 🙂7/18/2013 | Katherine P. CommentMichael W.Roseville, CA0 0Having the line parallel to y=-4 tells you the slope (parallel lines have the same slope). Since there is no coefficient to the “x” value (ie a slope of zero : y= 0x – 4), the slope of your new line is also 0 (m=0).Now for the y intercept value: plug your m (slope) into the standard slope intercept formula y=mx+b and include your point that the new line passes through. You then get the following:3=0(3) +b0 times 3 is 0, so your equation becomes 3=bYour equation is y=mx +b : mx=0, so it becomes y=b or in this case y=3 7/18/2013 | Michael W. CommentClaribel C.Schertz, TX0 4A parallel line will have the same slope as y=-4. To better understand line y=-4 you must write it as the line equation (y=mx+b). In order to have y=-4, the slope (m) must be -4, x must equals 1 and the intercept (b) must be 0. The line equation the would be y=-4x+0. Now that you have the line equation, let’s find the parallel line that passes through (3,3). To find the parallel line equation you must substitute values y and x by (3,3) in the first line equation and determine the corresponding intercept.3=-4*3+b3=-12+b3+12=b15=bTherefore, the line equation for the line that passes through (3,3) and is parallel to y=-4 is:y=-4x+157/18/2013 | Claribel C. CommentCommentsNot meaning to disagree, but the line y=-4 is a horizontal line and therefore has a slope of zero (there is no “rise”), so the “m” must be zero. Any value of x would give you a y value of -4.Therefore the correct equation of the given line is y=0x – 4. A parallel line running through (3,3) would have the formula y=3.Your line would intersect y=-4 at (19/4, -4) or (4.75, -4).7/18/2013 | Michael W.

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