Question

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 ?

A.
5x − 3y = 0
B.
-x + 3y = 0
C.
-5x − 3y = 0
D.
3x + 5y = 0
E.
-3x + 5y = 0

Answer 1

The answer is C. -5x - 3y = 0

Answer 2

`- 5x - 3y = 0`

Step-by-step explanation

The line that passes through the origin has equation of the form:

y=mx

Where m is the slope.

Since the line is parallel to the line through A(-3, 0) and B(-6, 5), they have the same slope.

The slope is given by:

`m = (y_2-y_1)/(x_2-x_1)`

`m = (5 - 0)/( - 6 - - 3) = - (5)/(3)`

Hence the required equation is:

`y = - (5)/(3) x`

Multiply through by 3,

`3y = - 5x`

In standard form, the equation is

`- 5x - 3y = 0`