Question

Which of the point-slope equations below is correcto for the line that passes through points (6,5) and (3,3)? Check all that apply.

Answer 1

A, D

Explanation:

The slope is ...

... m = (change in y)/(change in x) = (5-3)/(6-3) = 2/3

The points are (3, 3) and (6, 5).

The point-slope form of the equation of a line with slope m through (h, k) is ...

... y -k = m(x -h)

In your problem, m = 2/3, eliminating choices B and F.

The points all have positive coordinates, so the x- and y-terms will all have minus signs—eliminating choices B, C, E.

The only remaining choices are A and D, one of which uses one point and the other of which uses the other point. They are both valid choices.

• A. y - 3 = 2/3(x - 3)
• D. y - 5 = 2/3(x - 6)