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

Question

asked Feb 2, 2022 235k views

2 Answers

Wstk · Answer 1 · 2022-02-06T05:52:38+0000

Answer:

$\displaystyle y=-(2)/(3)x+(5)/(3)$

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:

$\displaystyle m=(3-(-1))/(-2-4)=(4)/(-6)=-(2)/(3)$

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:

$\displaystyle y-(-1)=-(2)/(3)(x-(4))$

Simplify and distribute:

$\displaystyle y+1=-(2)/(3)x+(8)/(3)$

Subtract 1 from both sides. Therefore:

$\displaystyle y=-(2)/(3)x+(5)/(3)$