Chapter 13.7, Problem 17WE

To determine

To find : an equation of line described

Answer to Problem 17WE

The equation is $y=2x-1$

Explanation of Solution

Given information :

Line through $\left(1,1\right)$ and $\left(4,7\right)$

Formula used :

  $m=\frac{y-y_1}{x-x_1}$

Calculation :

To find the slope

  $\begin{array}{l}m=\frac{7-1}{4-1}\\ m=\frac{6}{3}\\ m=2\end{array}$

Then use the point and slope

Using $\left(1,1\right)$ , the equation is

  $\begin{array}{l}y-1=2\left(x-1\right)\\ y=2x-2+1\\ y=2x-1\end{array}$

Using $\left(4,7\right)$ , the equation is

  $\begin{array}{l}y-7=2\left(x-4\right)\\ y=2x-8+7\\ y=2x-1\end{array}$

Hence, the equation is $y=2x-1$ .