### Graphing a Line in Slope Intercept Form

Recall that the equation of a line is \begin{align*}y = mx + b\end{align*}

Let's graph the following equations.

- Graph \begin{align*}y = \frac{1}{3}x + 4\end{align*}
y=13x+4 on the Cartesian plane.

First, the Cartesian plane is the \begin{align*}x-y\end{align*}

Now we need to use the slope to find the next point on the line. Recall that the slope is also \begin{align*}\frac{rise}{run}\end{align*}

Now that we have three points, connect them to form the line \begin{align*}y = \frac{1}{3}x + 4.\end{align*}

- Graph \begin{align*}y = -4x -5.\end{align*}
y=−4x−5.

Now that the slope is negative, the vertical distance will “fall” instead of rise. Also, because the slope is a whole number, we need to put it over 1. Therefore, for a slope of -4, the line will fall 4 and run 1 OR rise 4 and run backward 1. Start at the \begin{align*}y-\end{align*}

- Graph \begin{align*}x = 5\end{align*}
x=5 .

Any line in the form \begin{align*}x = a\end{align*}

To graph a horizontal line, \begin{align*}y = b\end{align*}

### Examples

#### Example 1

Earlier, you were asked to write an equation for the cost of a data plan, and determine how much your bill will be if you use 4.5 GB of data a month.

If *x* is the number of GB of data you use in a month and *y* is the total cost you pay, then the equation for the cell-phone plan would be \begin{align*}y=7.5x + 60\end{align*}

So your bill for the month would be $93.75.

#### Example 2

Graph the following lines.

- \begin{align*}y = -x + 2\end{align*}
y=−x+2 (Plot (0, 2) and the slope is -1, which means you fall 1 and run 1) - \begin{align*}y = \frac{3}{4}x - 1\end{align*}
y=34x−1 (Plot (0, -1) and then rise 3 and run 4 to the next point, (4, 2)) - \begin{align*}y = -6\end{align*}
y=−6 (Plot -6 on the \begin{align*}y-\end{align*}axis and draw a horizontal line)

All answers are on the same grid below.

### Review

Graph the following lines in the Cartesian plane.

- \begin{align*}y = -2x -3\end{align*}
- \begin{align*}y = x + 4\end{align*}
- \begin{align*}y = \frac{1}{3}x - 1\end{align*}
- \begin{align*}y = 9\end{align*}
- \begin{align*}y = - \frac{2}{5}x + 7\end{align*}
- \begin{align*}y = \frac{2}{4}x - 5\end{align*}
- \begin{align*}y = -5x -2\end{align*}
- \begin{align*}y = -x\end{align*}
- \begin{align*}y = 4\end{align*}
- \begin{align*}x = -3\end{align*}
- \begin{align*}y = \frac{3}{2}x + 3\end{align*}
- \begin{align*}y = - \frac{1}{6}x - 8\end{align*}
- Graph \begin{align*}y = 4\end{align*} and \begin{align*}x = -6\end{align*} on the same set of axes. Where do they intersect?
- If you were to make a general rule for the lines \begin{align*}y = b\end{align*} and \begin{align*}x = a\end{align*}, where will they always intersect?
- The cost per month, \begin{align*}C\end{align*} (in dollars), of placing an ad on a website is \begin{align*}C = 0.25x + 50,\end{align*}where \begin{align*}x\end{align*} is the number of times someone clicks on your link. How much would it cost you if 500 people clicked on your link?

### Answers for Review Problems

To see the Review answers, open this PDF file and look for section 2.6.