Question

find an equation for the line with the given properties. Express in slope intercept form.Perpendicular to the line x-7y=-3, containing the point (0,8). simplify the answer

Answer 1

The line is perpendicular to the line:

`x-7y=-3`

We can rewrite the equation in the slope-intercept form to be:

`\begin{gathered} 7y=x+3 \\ y=(1)/(7)x+(3)/(7) \end{gathered}`

This equation compared to the slope-intercept form will give the slope as follows:

`\begin{gathered} y=mx+b,m=slope \\ \therefore \\ m=(1)/(7) \end{gathered}`

Recall that perpendicular lines have slopes that are negative reciprocals. Thus:

`m_1=-(1)/(m_2)`

Hence, the slope of the required line will be:

`m=-7`

Given that we have the point the line passes through given, we can put the equation in the point-slope form:

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

At the point (0, 8), we have the equation to be:

`\begin{gathered} y-8=-7(x-0) \\ y-8=-7x \end{gathered}`

In the slope-intercept form, the equation of the line will be:

`y=-7x+8`