Use the given conditions to write an equation for the line in point-slope form.
-Passing through $( - 7 , - 7 )$ and $( - 5 , - 4 )$
A) $y + 7 = \frac { 3 } { 2 } ( x + 7 )$ or $y + 4 = \frac { 3 } { 2 } ( x + 5 )$
B) $y + 7 = \frac { 3 } { 2 } ( x + 5 )$ or $y + 4 = \frac { 3 } { 2 } ( x + 7 )$
C) $y - 7 = \frac { 3 } { 2 } ( x - 7 )$ or $y - 4 = \frac { 3 } { 2 } ( x - 5 )$
D) $y + 7 = \frac { 3 } { 2 } x - 7$ or $y + 4 = \frac { 3 } { 2 } x + 7$

Question

Quizplus · Accepted Answer

The slope of the line passing through $(-7, -7)$ and $(-5, -4)$ is $\frac{-4 - (-7)}{-5 - (-7)} = \frac{3}{2}$. The point-slope form of a line is $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line. Substituting the given points and the slope into this formula, we get the equations $y + 7 = \frac{3}{2}(x + 7)$ and $y + 4 = \frac{3}{2}(x + 5)$, which matches choice A.

Use the Given Conditions to Write an Equation for the Line