Question

Write the equation parallel to y=5x+1 that passes through (-1,-16).

Answer 1

`y = 5x -11`

Step-by-step explanation:

Given

`y = 5x + 1` -- equation

`(x,y) = (-1,-16)`

Required

Determine the equation parallel to the given equation and passes through the given point

An equation has a general form:

`y = mx + b`

Where:

`m = slope`

First, we need the slope of the required equation

Since the required equation is parallel to
`y = 5x + 1`, then they have the same slope

So, the slope m of the required equation is:

`m = 5`

Next, we determine the equation using:

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

Where

`m = 5`

`(x,y) = (-1,-16)`

So, we have:

`y - (-16) = 5(x - (-1))`

`y +16 = 5(x +1)`

Open bracket:

`y +16 = 5x +5`

Collect Like Terms

`y = 5x +5 - 16`

`y = 5x -11`