Question

What is the equation of the line that passes through (4, -1) and (-2, 3)?

Answer 1

Answer:

$\displaystyle y=-\frac{2}{3}x+\frac{5}{3}$

Step-by-step explanation:

We want to find the equation of the line that passes through the two points:

(4, -1) and (-2, 3).

First, we will find the slope of the two points. So:

$\displaystyle m=\frac{3-(-1)}{-2-4}=\frac{4}{-6}=-\frac{2}{3}$

Now, we will use the point-slope form given by:

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

Use either point. I'm going to use (4, -1). So, substitute:

$\displaystyle y-(-1)=-\frac{2}{3}(x-(4))$

Simplify and distribute:

$\displaystyle y+1=-\frac{2}{3}x+\frac{8}{3}$

Subtract 1 from both sides. Therefore:

$\displaystyle y=-\frac{2}{3}x+\frac{5}{3}$

Answer 2

Answer:

3--1/-2-4=4/-6=2/-3

y=-2/3x+b

-2*-2/3=4/3

3-4/3=5/3

y=-2/3x+5/3

Step-by-step explanation: