Question

In the following exercises, find the equation of a line with a given slope containing the given point. Write the equation in slope-intercept form.

A horizontal line containing$\left(-2,7\right)$.

Short answer

The slope-intercept form of the equation of the horizontal line that passes through the point $\left(-2,7\right)$is $y=7$or$y=0x+7$.

Step-by-step solution

Given information

Here the line is a horizontal line and passes through the point $\left(-2,7\right)$.

The point-slope form of a line equation that passes through the point$\left(x_1,y_1\right)$with slope$m$is$y-y_1=m\left(x-x_1\right)$.

Simplify

The slope of a horizontal line is $m=0$.

Here, $\left(x_1,y_1\right)=\left(-2,7\right)$.

Substitute these values in$y-y_1=m\left(x-x_1\right)$.

$\begin{array}{rcl}y-7& =& 0\left(x-\left(-2\right)\right)\\ y-7& =& 0\\ y& =& 7\end{array}$

The line equation is$y=7.$