Question

A
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 AB?
OA. 5x - 3y = 0
B. -* + 3y = 0
c. 5x - 3y = 0
D. 3x + 5y = 0
E. -3x + 5y = 0

Answer 1

Answer:

B. 5x + 3y = 0

Step-by-step explanation:

Parallel lines have the same slope.

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points A(-3, 0) and B(-6, 5). Substitute:

$m=\dfrac{5-0}{-6-(-3)}=\dfrac{5}{-3}=-\dfrac{5}{3}$

The line passes through the origin, therefore the y-intercept is equal to 0.

Therefore we have the equation:

$y=-\dfrac{5}{3}x$

Convert to the standard form $Ax+By=C$

$y=-\dfrac{5}{3}x$         multiply both sides by 3

$3y=-5x$                add 5x to both sides

$5x+3y=0$