Chapter 8.7, Problem 29PPS

To determine

To calculate: To graph $3x+4y=12$ using the slope and y-intercept

Answer to Problem 29PPS

Graph for the equation is plotted.

Explanation of Solution

Given information: Equation is $3x+4y=12$

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Calculation:

Equation is given as

  $3x+4y=12$

Rewriting the above equation,

  $\begin{array}{l}4y=-3x+12\\ y=-\frac{3}{4}x+\frac{12}{4}\\ y=-\frac{3}{4}x+3\end{array}$

Comparing the above equation to slope intercept form of line $y=mx+c$ , slope and Y-intercept are

  $\begin{array}{l}m=-\frac{3}{4}\\ c=3\end{array}$

Thus, y-intercept is at $\left(0,3\right)$ , which is the first point

Also, $m=-\frac{3}{4}$ , this means that one will rise3(up) and run4(to the left)

Thus, other point is $\left(-4,6\right)$

On plotting the graph,