Math

QuestionFind the slope-intercept form of the line through the points (2,1)(2,-1) and (4,5)(4,5).

Studdy Solution

STEP 1

Assumptions1. We have two points (,1)(,-1) and (4,5)(4,5). . We need to find the equation of the line passing through these points in slope-intercept form, which is y=mx+by = mx + b where mm is the slope and bb is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formulam=y2y1x2x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Now, plug in the given values for x1x1, y1y1, x2x2, and y2y2 to calculate the slope.
m=5(1)2m = \frac{5 - (-1)}{ -2}

STEP 4

implify the equation to calculate the slope.
m=62m = \frac{6}{2}

STEP 5

Calculate the slope.
m=3m =3

STEP 6

Now that we have the slope, we can find the y-intercept bb by rearranging the slope-intercept form of the equation y=mx+by = mx + b to solve for bbb=ymxb = y - mx

STEP 7

Plug in the values for mm, xx, and yy from one of the given points. Let's use the point (2,1)(2,-1)b=13(2)b = -1 -3(2)

STEP 8

Calculate the y-intercept bb.
b=16=7b = -1 -6 = -7

STEP 9

Now that we have the slope mm and the y-intercept bb, we can write the equation of the line in slope-intercept formy=mx+by = mx + b

STEP 10

Plug in the values for mm and bb to write the equation of the line.
y=3x7y =3x -7The equation of the line passing through the points (2,)(2,-) and (4,5)(4,5) is y=3x7y =3x -7.

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