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.
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Identify the slope and y-intercept:
- The slope (\(m\)) is \( \frac{1}{5} \).
- The y-intercept (\(b\)) is \( 1 \).
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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.
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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 \((1, 1.2)\).
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Plot the second point:
- Plot the point \((1, 1.2)\).
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Draw the line:
- Connect the points with a straight line, extending it in both directions.
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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.