Chapter 1.3, Problem 58E

To determine

Find an equation of a line.

Answer to Problem 58E

  $\boxed{y=4}$

Explanation of Solution

Given information:

Find an equation of the line passing through the points. Sketch the line

  $\left(-1,4\right),\left(6,4\right)$

Calculation:

Consider the given points.

  $\left(-1,4\right),\left(6,4\right)$

The slope of non vertical line through $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is,

  $m=\frac{y_2-y_1}{x_2-x_1}$ when $x_1\ne x_2$

Substitute the given point in above expression,

  $\begin{array}{l}m=\frac{4-4}{6-\left(-1\right)}\\ =\frac{0}{\begin{array}{l}7\\ m=0\end{array}}\end{array}$

Slope of non vertical line through $\left(-1,4\right)$ and $\left(6,4\right)$ is $m=0$

Now

The equation of the line slope $m$ passing through the point $\left(x_1,y_1\right)$ by this formula,

  $y-y_1=m\left(x-x_1\right)$

Put $m=0$ and $\left(-1,4\right)$ in above equation,

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-4=0\left(x-\left(-1\right)\right)\\ y-4=0\left(x+1\right)\\ y-4=0\end{array}$

Now add $4$ both sides.

  $\begin{array}{l}y-4+4=0+4\\ y=4\end{array}$

Now draw the graph of line,

  

Hence the slope intercepts form of line passing through the points $\left(-1,4\right)$ and $\left(6,4\right)$ is $\boxed{y=4}$