Graphing by Using the y-intercept and Slope

Graph $f (x) = - \frac{2}{3} x + 5$ using the y-intercept and slope.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Evaluate the function at $x = 0$ to find the y-intercept. The output value when $x = 0$ is 5, so the graph will cross the y-axis at $(0, 5) .$
According to the equation for the function, the slope of the line is $- \frac{2}{3} .$ This tells us that for each vertical decrease in the “rise” of $- 2$ units, the “run” increases by 3 units in the horizontal direction. We can now graph the function by first plotting the y-intercept on the graph in Figure 13. From the initial value $(0, 5)$ we move down 2 units and to the right 3 units. We can extend the line to the left and right by repeating, and then drawing a line through the points.

Figure 13 Graph of $f (x) = −2 / 3 x + 5$ and shows how to calculate the rise over run for the slope.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find a point on the graph we drew in Example 12 that has a negative x-value.

How did it go?