Question

Find the equation (in terms of x) of the line through the points (-4,2) and (3,-5)

Y=

Answer 1

Answer: y = -x-2

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Step-by-step explanation:

First we need the slope

`(x_1,y_1) = (-4,2) \text{ and } (x_2,y_2) = (3,-5)\\\\m = (y_(2) - y_(1))/(x_(2) - x_(1))\\\\m = (-5 - 2)/(3 - (-4))\\\\m = (-5 - 2)/(3 + 4)\\\\m = (-7)/(7)\\\\m = -1\\\\`

Then we can find the y intercept using the coordinates of (x,y) = (-4,2)

y = mx+b

2 = -1(-4)+b

2 = 4+b

2-4 = b

-2 = b

b = -2

Alternatively, you can use the other point (x,y) = (3,-5) and m = -1.

Because m = -1 and b = -2, we go from y = mx+b to y = -1x+(-2) which simplifies to y = -x-2