Question

Find+Graph the equation parallel to y=4x-5 with a x-intercept of -5.

Answer 1

Line equations can be written in slope-intercept form. The slope-intercept form is

`y=mx+b`

Where m represents the slope and b the y-intercept.

The given line is

`y=4x-5`

Comparing this equation with the slope-intercept form, we have a line with slope equal to 4 and y-intercept equals to -5.

Parallel lines have the same slope, then, the equation for the line we want has the following form

`y=4x+b`

The x-intercept is -5, then, this means that x = -5 when y = 0. We can substitute those values in our form to find the coefficient b.

`\begin{gathered} 0=4\cdot(-5)+b \\ 0=-20+b \\ -b=-20 \\ b=20 \end{gathered}`

This means that our line is

`y=4x+20`

Graphing this equation, we have