Question

Find, in standard form, the equation of the line that is parallel to y = 4x + 2 and passes through (5, -5)

Answer 1

The equation of the line that is parallel to

`y=4x+2`

and passes through (5,-

Step-by-step explanation:

We want to find the standard form equation of the line that is parallel to

`y=4x+2\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(1)`

and passes through the points (5, -5)

The equation of the line given above has slope of 4 units, and y-intercept of 2.

Any equation with the slope 4 units and a different y-intercept from 2 - is a parallel line with the line in equation (1).

Let this parallel line be:

`y=4x+b\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(2)`

Since this line passes through (5, -5), we have x = 5, and y = -5. Substituting these valeus of x and y in equation (2), we can easily find the value of the y-intercept b

`\begin{gathered} -5=4(5)+b \\ \\ -5=20+b \\ \\ \text{Subtract 20 from both sides} \\ -5-20=b \\ b=-25 \end{gathered}`

Therefore, the equation of the line is:

`y=4x-25`