Chapter 13, Problem 23CR

To determine

To find: The equation of a straight line passing through the given two-points.

Answer to Problem 23CR

The equation of a straight line passing through $\left(-1,2\right)$ and $\left(3,10\right)$ is $2x-y=0$ .

Explanation of Solution

Given information: The points through which a line passes are $\left(-1,2\right)$ and $\left(3,10\right)$ .

Calculation:

The equation to determine the slope of the line passing through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute $-1$ for $x_1$ , $2$ for $x_2$ , $3$ for $y_1$ and $10$ for $y_2$ in the above expression.

  $\begin{array}{c}m=\frac{10-2}{3-\left(-1\right)}\\ =\frac{8}{4}\\ =2\end{array}$

The equation for straight line is:

  $y=mx+b$

Substitute $2$ for $m$ and $0$ for $b$ in the above expression.

  $\begin{array}{c}y=2x+0\\ 2x-y=0\end{array}$

Therefore, the equation of a straight line passing through $\left(-1,2\right)$ and $\left(3,10\right)$ is $2x-y=0$ .