Question

What is an equation of the line that passes through the point (-3, -7) and is parallel to the line 2x-3y=24 Please

Answer 1

Answer: y =
`(2)/(3)`x - 5

Explanation:

We are given a point and a given line. First, we will transform the given equation into a slope-intercept equation. This is y= mx + b, where m is the slope and b is the y-intercept.

2x - 3y = 24

2x - 24 = 3y

y =
`(2)/(3)`x - 8

Now, we will take the slope from the line we got above since parallel lines have the same slope.

y =
`(2)/(3)`x + b

Next, we will create a point-slope form equation. Then, we will simplify.

y - y1 = m(x - x1)

y - - 7 =
`(2)/(3)`(x - - 3)

y + 7 =
`(2)/(3)`(x + 3)

y + 7 =
`(2)/(3)`x + 2

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

I have also graphed this line, the parallel line, and the given point. See attached.