To derive the new equation of a line after a change in slope, we can start from the general form of the equation of a line:
\[ y = mx + b \]
Here, \( m \) represents the slope and \( b \) represents the y-intercept.
In your case, the slope is changed to \( \frac{1}{5} \), while the y-intercept \( b \) remains unchanged. Therefore, the resulting equation of the new graph will be:
\[ y = \frac{1}{5}x + b \]
To specify the exact equation, you would need the value of \( b \) (the y-intercept) from the original graph. Once you have that value, you can substitute it into the equation above to get the final equation of the new graph.
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