Question

select the equation of the line that passes through (-5, -3) and (-7, -12).
a) $y = \frac{5}{4}x - \frac{13}{4}$
b) $y = \frac{5}{4}x + \frac{13}{4}$
c) $y = \frac{9}{2}x + \frac{39}{2}$
d) $y = \frac{9}{2}x + 47$

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-5,y_1 = - 3,x_2=-7,y_2=-12$. So $m=\frac{-12-(-3)}{-7-(-5)}=\frac{-12 + 3}{-7 + 5}=\frac{-9}{-2}=\frac{9}{2}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-5,-3)$ and $m = \frac{9}{2}$, we have $y-(-3)=\frac{9}{2}(x-(-5))$, which simplifies to $y + 3=\frac{9}{2}(x + 5)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y+3=\frac{9}{2}x+\frac{45}{2}$. Then subtract 3 from both sides: $y=\frac{9}{2}x+\frac{45}{2}-3=\frac{9}{2}x+\frac{45 - 6}{2}=\frac{9}{2}x+\frac{39}{2}$.

Answer:

C. $y=\frac{9}{2}x+\frac{39}{2}$