Question

Write an equation of the line that passes through (2,-5) and is parallel to the line 2y = 3x + 10.

y =?

Answer 1

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

Explanation:

1) Set the line given to you in y = mx + b form:

2y = 3x + 10

`(2y)/(2) = (3x)/(2) + (10)/(2)` (divide everything by 2)

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

2) Since the lines are parallel, the slopes must be the same. Now that we know the slope of the line, use point slope form [
`y - y_(1) = m(x - x_(1))` ] to find the equation of the line using the points given:

y - (-5) =
`(3)/(2)`( x - (2)) - insert the values into the equation

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

y =
`(3)/(2)x - 8` - subtract 5 from both sides