Question

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

y=

Answer 1

2y = 3x + 10 --> almost there already, just divide everything by 2 to get y by itself. y = 3/2x + 5 --> now you have it in the y=mx + b form, so your slope is 3/2 They asked for the parallel line, remember parallel lines have the same slope, therefore you use the same slope.

Answer 2

`y = 1.5x - 8`

Explanation:

Step 1: Solve for y in the first equation

`2y = 3x + 10`

`(2y)/(2)=(3)/(2)x + (10)/(2)`

`y = 1.5x + 5`

Step 2: Determine the important aspects

We know that our line is parallel to the other line that has a slope of 1.5 which means that our slope is also going to be 1.5. We also know that our line crosses the point (2, -5) which means that we can use the point slope form to determine our equation

Point Slope Form →
`(y-y_1) = m(x - x_1)`

Step 3: Plug in the information and solve

`(y-(-5)) = 1.5(x - 2)`

`y + 5 = 1.5x -3`

`y + 5 - 5 = 1.5x -3 - 5`

`y = 1.5x - 8`

Answer:
`y = 1.5x - 8`