Using the slope and the y-intercept, graph the line represented by the following equation. Then select the correct graph. 3y = 2x - 6

Accepted Solution

First, let's write the given equation in slope-intercept form: y = mx + b

In slope-intercept form, the slope of the line is m, and the y-intercept is b. The slope is a measure of how steep the graph is at any point and is found by doing rise over run. This means the change in y values divided by the change in x values. Next, y-intercept is just where the graph crosses the y axis.

All we need to do to get the equation in slope-intercept form is to divide each term by 3. This will isolate the y.

[tex]y= \frac{2}{3}x-2 [/tex]

As you can see, the slope of the line is 2/3, and the y-intercept is -2.

To graph the line, plot a point at (0,-2). This is the point where the graph crosses the y axis. Then from that point, count up two and right 3. Plot a point here as well. Lastly, connect the two points with a straight line.

See attached picture for the graph.