The equation you provided, \(5x - 6y = 8\), is a linear equation in two variables (x and y). To express this equation in a more useful form, such as the slope-intercept form \(y = mx + b\), we can solve for \(y\).
Here’s how you can do it:
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Start with the original equation: \[ 5x - 6y = 8 \]
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Subtract \(5x\) from both sides: \[ -6y = -5x + 8 \]
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Divide every term by \(-6\): \[ y = \frac{5}{6}x - \frac{8}{6} \]
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Simplify \(-\frac{8}{6}\) to \(-\frac{4}{3}\): \[ y = \frac{5}{6}x - \frac{4}{3} \]
Now, the equation is in slope-intercept form, where the slope \(m = \frac{5}{6}\) and the y-intercept \(b = -\frac{4}{3}\).
If you want to find specific values of \(x\) and \(y\) that satisfy the equation or graph it, please provide additional details!