Question

Write an equation in point-slope form of the line that passes through the given point and is parallel to the graph of the given equation

Answer 1

The equation of the line is:

`y -1= 5(x - 2)`

Explanation:

Given

Pass through
`(2,-1)`

Parallel to:
`y= 5x - 2`

Required

Determine the equation in point slope form

An equation has a general form:

`y = mx + c`

Where:

`m = slope`

Compare:
`y = mx + c` to
`y= 5x - 2`

we have:

`m = 5`

Since the line is parallel to
`y= 5x - 2`, then they have the same slope of 5

The line equation is then calculated using:

`y -y_1= m(x - x_1)`

Where

`m = 5`

`(x_1,y_1) =`
`(2,-1)`

So, we have:

`y -1= 5(x - 2)`