Question

Which equations in point-slope form are equations of the line that pass through the points (−7, 5) and (−4, 1)?



Choose exactly two answers that are correct.

Answer 1

\[Slope = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1} } = \frac{ 1 - 5 }{ -4 + 7 } = \frac{ -4 }{ 3 }\]

Line equation:

y = mx + b

m = y - b / x

y-b/x = -4/3
3y - 3b = -4x

3y = -4 x + 3 b , at ( -4 , 1)

3 = 16 + 3 b , 3b = -13
b = -13/3

3y = -4x - 13

y = -4x/3 - 13/3

Now, move to the question:

A ) y = -3/4x + 15/ 4 + 7 , y = -3/4x + 43/4 (x)
b) y = -4/3 x + -28/3 + 5 , y = -4/3 x - 13/3 ( OK )
c) No as x will be multilied times -3/4 (different coefficient than -4/3) we could have used this in A too
d) y = -4/3 * x - 13/3 (OK)

so collection set is {B, D}

Answer 2

Thank you so much!