Chapter 4.2, Problem 57SR

To determine

To graph the equation $y=3x+2$

Explanation of Solution

Given Information:

Equation of line is $y=3x+2$

Concept Used:

The slope-intercept form of a linear equation is

  $\begin{array}{l}y=mx+c\\ where\\ m=\frac{rise}{run}\to slope\\ c\to y-\mathrm{intercept}\\ \end{array}$

Graph:

Given equation $y=3x+2$

Comparing it with the slope-intercept form ,

We have,

  $\begin{array}{l}y=mx+c\mathrm{..................................}[slope-\mathrm{intercept}]\\ y=3x+\mathrm{2..................................}[Original\_equation]\\ m=\frac{rise}{run}=\frac{3}{1}\\ c=\mathrm{2..........................................}[Comparing]\\ \end{array}$

Now, graph the equation

Step 1. Plot the y-intercept (0,2)

Step 2. The slope is $\frac{rise}{run}=\frac{3}{1}$ . From (0,2) move up 3 units and then move right 1 unit . Plot the point (1,5).

Step 3. Draw a line through the two points (0,2) and (1,5) .

The resulting graph is shown below: