Suppose a company had the slope and \begin{align*}y\end{align*}

### Graphs Using Slope-Intercept Form

The slope of a line describes how to navigate from one point on the line to another, and the \begin{align*}y\text{-intercept}\end{align*}

#### Let's graph the following equations:

- \begin{align*}y=2x+5.\end{align*}
y=2x+5.

The equation is in slope-intercept form. To graph the solutions to this equation, you should start at the \begin{align*}y\text{-intercept}.\end{align*}

- \begin{align*}y=-3x+5.\end{align*}
y=−3x+5.

Using the definition of slope-intercept form, this equation has a \begin{align*}y\text{-intercept}\end{align*}

#### Slopes of Parallel Lines

**Parallel lines** will never **intersect**, or cross. The only way for two lines never to cross is if the method of finding additional coordinates is the same.

Therefore, it's true that parallel lines have the same slope.

#### Let's use this information to determine the slope of any line parallel to \begin{align*}y=\text{-}3x+5\end{align*}y=-3x+5 :

Because parallel lines have the same slope, the slope of any line parallel to \begin{align*}y=\text{-}3x+5\end{align*}

### Examples

#### Example 1

Earlier, you were told that a company had the slope and \begin{align*}y\end{align*}

The company could graph the line by graphing the \begin{align*}y\end{align*}

#### Example 2

Graph \begin{align*}y=-\frac{2}{5}x\end{align*}

First, graph the \begin{align*}y\end{align*}

Next, the slope is \begin{align*}-\frac{2}{5}\end{align*}

### Review

Plot the following equations on a graph.

- \begin{align*}y=2x+5\end{align*}
y=2x+5 - \begin{align*}y=-0.2x+7\end{align*}
y=−0.2x+7 - \begin{align*}y=-x\end{align*}
y=−x - \begin{align*}y=3.75\end{align*}
- \begin{align*}\frac{2}{7} x-4=y\end{align*}
- \begin{align*}y=-4x+13\end{align*}
- \begin{align*}-2+\frac{3}{8} x=y\end{align*}
- \begin{align*}y=\frac{1}{2}+2x\end{align*}

In 9 – 16, state the slope of a line parallel to the given line.

- \begin{align*}y=2x+5\end{align*}
- \begin{align*}y=-0.2x+7\end{align*}
- \begin{align*}y=-x\end{align*}
- \begin{align*}y=3.75\end{align*}
- \begin{align*}y=-\frac{1}{5}x-11\end{align*}
- \begin{align*}y=-5x+5\end{align*}
- \begin{align*}y=-3x+11\end{align*}
- \begin{align*}y=3x+3.5\end{align*}

### Review (Answers)

To see the Review answers, open this PDF file and look for section 4.10.