Question

Graph this line using the slope and y
-intercept:
y
=
1/5
x
+
1

Answer 1

To graph the line given by the equation \( y = \frac{1}{5}x + 1 \), we need to identify the slope and the y-intercept from the equation.

1. **Identify the slope and y-intercept**:
- The slope (\(m\)) is \( \frac{1}{5} \).
- The y-intercept (\(b\)) is \( 1 \).

2. **Plot the y-intercept**:
- Start by plotting the point where the line crosses the y-axis. Since the y-intercept is \(1\), plot the point \((0, 1)\) on the graph.

3. **Use the slope to find another point**:
- The slope \(m = \frac{1}{5}\) means that for every increase of \(1\) unit in \(x\), \(y\) increases by \(\frac{1}{5}\) units.
- From the point \((0, 1)\), move \(1\) unit to the right (to \(x = 1\)) and \( \frac{1}{5} \) units up (to \(y = 1 + \frac{1}{5} = 1.2\)). This gives you the point \((1, 1.2)\).

4. **Plot the second point**:
- Plot the point \((1, 1.2)\).

5. **Draw the line**:
- Connect the points with a straight line, extending it in both directions.

6. **Optional**: You can find additional points by repeating the slope method. For example:
- From \((1, 1.2)\), move \(1\) unit right to \(2\) and \( \frac{1}{5} \) units up to \(1.4\), giving you the point \((2, 1.4)\).

You should now have two or more points plotted along with the line passing through them. The line will be a straight line that represents the equation \(y = \frac{1}{5}x + 1\).

Here’s a simple representation of what the graph may look like:

\[
\text{Graph:}
\begin{align*}
| \\
| * (1, 1.2) \\
| * (0, 1) \\
| * (2, 1.4) \\
|_________________________________
\]

Remember, the line will continue infinitely in both directions.