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

The second option is correct. The point slope form of AB is
`y+1=(-3)/(2)(x-1)`.

Explanation:

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

Slope of a line is

`m=(y_2-y_1)/(x_2-x_1)`

Slope of AB is

`m=(-1-5)/(1-(-3))`

`m=(-6)/(4)`

`m=(-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
`(-3)/(2)` and the point is (-3,5). The point slope form of AB is

`y-5=(-3)/(2)(x+3)`

Case 1: The slope of the line is
`(-3)/(2)` and the point is (1,-1). The point slope form of AB is

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

Therefore the point slope form of AB is
`y+1=(-3)/(2)(x-1)`. Option 2 is correct.