Chapter 3.4, Problem 32PPS

To determine

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

Answer to Problem 32PPS

Graph of the given equation:

  

y-intercept of line is 2.

Slope of the line is $\frac{2}{3}.$

Explanation of Solution

Given information: We have given linear equation $3y-6=2x$

Solution:

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

Plugging x=0 in given equation

  $\begin{array}{l}3y-6=2(0)\\ \Rightarrow 3y-6=0\end{array}$

Add 6 on both sides and divide by 3.

  $\begin{array}{l}3y-6+6=0+6\\ \Rightarrow 3y=6\\ \Rightarrow y=2\end{array}$

We got first coordinate (0,2).

Now, plugging x=3 in given equation

  $\begin{array}{l}3y-6=2(3)\\ \Rightarrow 3y-6=6\end{array}$

Add 6 on both sides and dividing by 3.

  $\begin{array}{l}3y-6+6=6+6\\ \Rightarrow 3y=12\\ \Rightarrow y=4\end{array}$

So, we got second coordinate (3,4).

Draw a line by joining the points $\left(0,2\right)$ and $(3,4)$

  

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

Now, if we go 2 units up and 3 units right, we get another coordinate (3,4).

So the slope will be

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

Therefore, slope of the line is $\frac{2}{3}.$