line ab passes through a(-3, 0) and b(-6, 5). what is the equation of the line that passes through the…

Explanation:

Step1: Find the slope of line AB

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $A(-3,0)$ and $B(-6,5)$, then $m_{AB}=\frac{5 - 0}{-6-(-3)}=\frac{5}{-3}=-\frac{5}{3}$.

Step2: Determine the slope of the required line

Parallel lines have equal slopes. The line passes through the origin $(0,0)$ and has a slope $m = -\frac{5}{3}$. Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(0,0)$, we get $y-0 = -\frac{5}{3}(x - 0)$, which simplifies to $y=-\frac{5}{3}x$.

Step3: Convert to general form

Multiply through by 3 to get $3y=-5x$, or $5x + 3y = 0$. Multiply by - 1 gives $-5x-3y = 0$.

Answer:

C. -5x - 3y = 0