Question

Which of the following point-slope form equations could be produced with the points (6, 1) and (3, -2)?

y + 1 = 1(x - 6)

y - 1 = -1(x - 6)

y + 1 = 1(x + 6)

y - 1 = 1(x - 6)

Answer 1

• Point-Slope form:
  `y-y_1=m(x-x_1)`, with m = slope and
  `(x_1,y_1)` as a coordinate.
• Slope formula:
  `(y_2-y_1)/(x_2-x_1)`

So firstly, we have to find the slope. Using our two points, we will solve for the slope as such:

`(1-(-2))/(6-3)=(3)/(3)=1`

So now that we have the slope, we are going to be using the slope formula again, except that we are only using coordinate (6,1) and have the slope formula equal to 1. Our equation looks as such:
`(y-1)/(x-6)=1`

For this, multiply both sides by (x - 6) and your point-slope form is
`y-1=1(x-6)`, or the last option.