Q. 109 - Precalculus Enhanced with Graphing Utilities

Question

Write an equation of each line. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer.

Step-by-Step Solution

Answer

The equation of line is: $y=-\frac{1}{3}x+1$

Step 1. Given information

Graph of line is: 

Step 2. Finding slope of the line.

The two points on the line are: $(0,1) \mathrm{and} (3,0)$

Slope of the line is given by,

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{0-1}{3-0} \\ \Rightarrow m=-\frac{1}{3} \end{gathered}$$

Step 3. Finding y-intercept of the line.

From the graph, y-intercept, $b=1$

Step 4. Finding equation of the line

Slope-intercept form of the line is: $y=mx+b$

Substituting slope and y-intercept in the equation above, we get, $y=-\frac{1}{3}x+1$