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 ab?
a. 5x − 3y = 0
b. -x + 3y = 0
c. -5x − 3y = 0
d. 3x + 5y = 0
e. -3x + 5y = 0

Option C. -5x − 3y = 0

Step-by-step explanation:

we know that

AB passes through A(-3, 0) and B(-6, 5)

step 1

Find the slope AB

The formula to calculate the slope between two points is equal to

substitute

step 2

Find the slope of the line that passes through the origin and is parallel to AB

remember that

If two lines are parallel, then their slopes are the same

therefore

The slope is

step 3

Find the equation of the line that passes through the origin and is parallel to AB

The equation in point slope form is equal to

we have

substitute

Multiply by 3 both sides to remove the fraction

29.5977692753

step-by-step explanation:

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18