Chapter 3.4, Problem 28PPS

To determine

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

Answer to Problem 28PPS

Graph of the given equation:

  

y-intercept of line is 3.

Slope of the line is -4/9.

Explanation of Solution

Given information: We have given linear equation $4x+9y=27$

Solution:

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

Plugging x=0 in given equation

  $\begin{array}{l}4(0)+9y=27\\ \Rightarrow 9y=27\end{array}$

Divide both sides by 9.

  $\begin{array}{l}\frac{9y}{9}=\frac{27}{9}\\ \Rightarrow y=3\end{array}$

We got first coordinate (0,3).

Now, plugging x=9 in given equation

  $\begin{array}{l}4(9)+9y=27\\ \Rightarrow 36+9y=27\end{array}$

Subtract 36 on both sides and dividing by 9.

  $\begin{array}{l}36+9y-36=27-36\\ \Rightarrow 9y=-9\\ \Rightarrow y=-1\end{array}$

So, we got second coordinate (9,-1).

Draw a line by joining the points $\left(0,3\right)$ and $(9,-1)$

  

From the graph, we can see that line crosses y-axis at 3.

Therefore, y-intercept is 3.

Now, if we go 4 units down and 9 units right, we get another coordinate (9,-1).

So the slope will be

Rise/Run = 3-(-1)/0-9 = -4/9.

Therefore, slope of the line is -4/9.