To rewrite the equation \(2x - 5y = 10\) in slope-intercept form (\(y = mx + b\)), we need to solve for \(y\).
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Start with the original equation: \[ 2x - 5y = 10 \]
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Subtract \(2x\) from both sides: \[ -5y = -2x + 10 \]
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Divide each term by \(-5\): \[ y = \frac{2}{5}x - 2 \]
Now, the equation is in the slope-intercept form \(y = mx + b\), where:
- \(m\) (the slope) is \(\frac{2}{5}\)
- \(b\) (the y-intercept) is \(-2\)
So, the slope is \(\frac{2}{5}\) and the y-intercept is \(-2\).
To select the correct graph, look for:
- A line with a slope that rises \(2\) units for every \(5\) units it moves to the right.
- The line crossing the y-axis at \(-2\).
This information should help you identify the correct graph corresponding to the equation.
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