Chapter 4, Problem 24SGR

To determine

To find:The equation of the line for the given condition.

Answer to Problem 24SGR

The equation of the straight line is $y=2x+11$ .

Explanation of Solution

Given:

The equation passes through points $\left(-4,3\right)$ and $\left(1,13\right)$

Calculation:

The standard form of line passing through two points is $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ .

Here $\frac{y_2-y_1}{x_2-x_1}$ is the slope of the straight line. $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are the points from which the straight line passes.

Substitute $\left(-4,3\right)$ for $\left(x_1,y_1\right)$ and $\left(1,13\right)$ for $\left(x_2,y_2\right)$ .

The equation of the straight line is

  $\begin{array}{l}y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\\ y-\left(3\right)=\frac{\left(13\right)-\left(3\right)}{\left(1\right)-\left(-4\right)}\left(x-\left(-4\right)\right)\\ y-3=\frac{10}{5}\left(x+4\right)\\ y=2x+8+3\\ y=2x+11\end{array}$

Therefore, the equation of the straight line is $y=2x+11$ .