Question

What is the equation of the line that is parallel to the given line and has an x-intercept of –3?

Answer 1

The correct choice is "y = (2/3)x + 2"

Answer 2

Option B

Explanation:

In the figure, attached, given line passes through two points ( 3, 1 ) and ( 0, 1 ).

So slope of the line will be =
`((y-y'))/((x-x'))`

=
`((1+1))/((3-0))`

=
`(2)/(3)`

Now a line which is parallel to this line will have same slope as (
`(2)/(3)` ) and equation will be y =
`(2)/(3)`x + c

Now it is given that this line passes through ( -3, 0 )

[ x-intercept given as (-3)]

We plug in the values in the equation to get the value of c

0 =
`(2)/(3)` ( -3) + 6

0 = -2 + c ⇒ c = 2

Therefore, equation will be y =
`(2)/(3)`x + 2

Option B is the answer.