What is the equation of the line that passes through the point $(5,3)$ and has a slope of $-\frac{4}{5}$ ?
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Step 1 ：The equation of a line in slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. We know the slope \(m\) and a point \((x, y)\) that the line passes through, so we can substitute these values into the equation to solve for \(b\).

Step 2 ：Substitute \(x = 5\), \(y = 3\), and \(m = -\frac{4}{5}\) into the equation \(y = mx + b\) to solve for \(b\).

Step 3 ：After substituting, we find that \(b = 7.0\).

Step 4 ：Substitute \(m = -\frac{4}{5}\) and \(b = 7.0\) back into the equation \(y = mx + b\) to get the final equation of the line.

Step 5 ：Final Answer: The equation of the line that passes through the point \((5,3)\) and has a slope of \(-\frac{4}{5}\) is \(y = -\frac{4}{5}x + 7\). So, the final answer is \(\boxed{y = -\frac{4}{5}x + 7}\).