Chapter 3, Problem 39SGR

To determine

To graph the equation then state the slope and y- intercept of line.

Answer to Problem 39SGR

Graph of the given equation:

  

Slope of the line is $-\frac{3}{4}$ .

y-intercept of line is 2.

Explanation of Solution

Given information: We have given linear equation $3x+4y=8$

Solution:

In order to graph the line, we need to get two points.

Plugging x=0 in given equation

  $\begin{array}{l}3(0)+4y=8\\ \Rightarrow 4y=8\end{array}$

Divide both sides by 4.

  $\begin{array}{l}\frac{4y}{4}=\frac{8}{4}\\ \Rightarrow y=2\end{array}$

We got first coordinate (0, 2).

Now, plugging x=4 in given equation

  $\begin{array}{l}3(4)+4y=8\\ \Rightarrow 12+4y=8\end{array}$

Subtract 12 on both sides and dividing by 4.

  $\begin{array}{l}12+4y-12=8-12\\ \Rightarrow 4y=-4\\ \Rightarrow y=-1\end{array}$

So, we got second coordinate (4,-1).

Draw a line by joining the points $\left(0,2\right)$ and $(4,-1)$

  

From the graph, we can see that line crosses y-axis at 2. Therefore, y-intercept is 2.

Now, if we go 3 units down and 4 units right, we get another coordinate (4,-1).

So the slope will be

  $\frac{Rise}{Run}=\frac{2-\left(-1\right)}{0-4}=-\frac{3}{4}$

Therefore, slope of the line is $-\frac{3}{4}$ .