Question

Which equation is a point slope form equation for line AB ? y+1=32(x−1) y+1=−32(x−1) Four-quadrant Cartesian graph with integer tickmarks from -9 to 9 (or -10 to 10) for x and y axes, with a straight line with arrowheads drawn through two points labeled A and B. Point A is at (-3,5) and point B is at (1,-1).

Answer 1

Answer:

The second option is correct. The point slope form of AB is $y+1=\frac{-3}{2}(x-1)$.

Step-by-step explanation:

The given points are A(-3,5) and B(1,-1).

Slope of a line is

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of AB is

$m=\frac{-1-5}{1-(-3)}$

$m=\frac{-6}{4}$

$m=\frac{-3}{2}$

The point slope form of a line is

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

Where, m is slope of the line.

Case 1: The slope of the line is $\frac{-3}{2}$ and the point is (-3,5). The point slope form of AB is

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

Case 1: The slope of the line is $\frac{-3}{2}$ and the point is (1,-1). The point slope form of AB is

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

Therefore the point slope form of AB is $y+1=\frac{-3}{2}(x-1)$. Option 2 is correct.