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:

$\begin{gathered} 7y=x+3 \\ y=\frac{1}{7}x+\frac{3}{7} \end{gathered}$

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

$\begin{gathered} y=mx+b,m=slope \\ \therefore \\ m=\frac{1}{7} \end{gathered}$

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

$m_1=-\frac{1}{m_2}$

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:

$y=-7x+8$