How do you write an equation in slope intercept form given (2, 4) and (1, –3)?

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Answer 1 · 2017-11-21T10:43:47

$y=7x-10$

See the explanation for the process.

First determine the slope using the slope formula:

$m=(y_2-y_1)/(x_2-x_1)$ ,

where:

$m$ is the slope, $(x_1,y_1)$ is one point, and $(x_2,y_2)$ is the second point.

Point 1: $(2,4)$

Point 2: $(1,-3)$

Plug the known values into the formula:

$m=(-3-4)/(1-2)$

Simplify.

$m=(-7)/(-1)$ $larr$ two negatives make a positive

$m=7$

Now determine the linear equation using the point-slope form:

$y-y_1=m(x-x_1)$ ,

where $y_1$ and $x_1$ are a point, and $m=7$

We can use one of the points from determining the slope. I'm going to use Point 1: $(2,4)$ .

Plug in the given point and slope.

$y-4=7(x-2)$ $larr$ point-slope form

We can solve the point-slope form for $y$ , which will give us the slope-intercept from:

$y=mx+b$ ,

where:

$m$ is the slope and $b$ is the y-intercept.

$y-4=7(x-2)$

Expand.

$y-4=7x-14$

Add $4$ to both sides.

$y=7x-14+4$

Simplify.

where the slope $(m)$ is $7$ and the y-intercept $(b)$ is $-10$ .