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

B

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=(\Delta y)/(\Delta x)=(-2-4)/(8-(-1))=(-6)/(9)=-(2)/(3)`

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

Substitute:

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

Simplify:

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

Therefore, our answer is B.