Question

Which of the following is a point-slope equation of a line that passes through the points (-1, 4) and (8,-2)?

A. y-4= -3/2(x+1)
B. y-4= -2/3(x+1)
C. y-4= 2/3(x+1)
D. y-4= -2/3(x-1)​

Answer 1

Answer:

B

Step-by-step explanation:

We want to find the point-slope equation of a line that passes through the points (-1, 4) and (8, -2).

Point-slope form is given by:

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

Where m is the slope and (x₁, y₁) is a point.

So, let's find the slope of the line first. We can use the slope formula:

$\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{-2-4}{8-(-1)}=\frac{-6}{9}=-\frac{2}{3}$

We can choose (-1, 4) as our point. So, (x₁, y₁) = (-1, 4).

Substitute:

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

Simplify:

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

Therefore, our answer is B.