Q. 49 - Precalculus Enhanced with Graphing Utilities

Question

Find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer.  

Containing the points $(1,3) and (-1,2)$

Step-by-Step Solution

Answer

The equation of line is $y=\frac{1}{2}x+\frac{5}{2}$

Step 1. Given Information

The given points are $(1,3) and (-1,2)$

Step 2. Calculation

Use the given points to find the slope of line.

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{2-3}{-1-1} \\ =\frac{-1}{-2} \\ =\frac{1}{2} \end{gathered}$$

Us ethe point slope equation to find the equation of line in slope intercept form.

$$\begin{gathered} y-y_1=m(x-x_1) \\ y-3=\frac{1}{2}(x-1) \\ y-3=\frac{1}{2}x-\frac{1}{2} \\ y=\frac{1}{2}x+\frac{5}{2} \end{gathered}$$