Math

QuestionFind xx for the line through (8,2)(-8,-2) and (x,2)(x, 2) with a slope of 33.

Studdy Solution

STEP 1

Assumptions1. The line passes through the points (8,)(-8,-) and (x,)(x,). The slope of the line is 33

STEP 2

The a line passing through two points (x1,y1)(x1, y1) and (x2,y2)(x2, y2) is given by the formulam=y2y1x2x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

We know that the slope of the line is 33, and the line passes through the points (8,2)(-8,-2) and (x,2)(x,2). So we can set up the equation3=2(2)x(8)3 = \frac{2 - (-2)}{x - (-8)}

STEP 4

implify the equation.
3=4x+83 = \frac{4}{x +8}

STEP 5

To isolate xx, we can cross multiply.
3(x+8)=43(x +8) =4

STEP 6

istribute 33 to xx and 88.
3x+24=43x +24 =4

STEP 7

Subtract 2424 from both sides of the equation to isolate 3x3x.
3x=4243x =4 -24

STEP 8

Calculate the right side of the equation.
3x=203x = -20

STEP 9

Divide both sides by 33 to solve for xx.
x=203x = \frac{-20}{3}So, the value of xx such that the line passing through the points (8,2)(-8,-2) and (x,2)(x,2) has a slope of 33 is x=203x = -\frac{20}{3}.

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