Question

line ab passes through a(-3, 0) and b(-6, 5). what is the equation of the line that passes through the origin and is parallel to line ab?
a. $5x - 3y = 0$
b. $-x + 3y = 0$
c. $-5x - 3y = 0$
d. $3x + 5y = 0$
e. $-3x + 5y = 0$

Explanation:

Step1: Calculate slope of AB

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{5 - 0}{-6 - (-3)} = \frac{5}{-3} = -\frac{5}{3}$

Step2: Use point-slope for parallel line

Parallel lines have equal slopes. Line passes through $(0,0)$, so use $y = mx$.
$y = -\frac{5}{3}x$

Step3: Rearrange to standard form

Multiply both sides by 3: $3y = -5x$
Rearrange terms: $5x + 3y = 0$ or $-5x - 3y = 0$

Answer:

C. $-5x - 3y = 0$