Write the equation of the line which has a slope of $\frac{4}{5}$ and passes through $(5,3)$. Write the answer in slope-intercept form.
\(\boxed{y = \frac{4}{5}x - 1}\)
Step 1 :Write the point-slope form of a linear equation: $y - y_1 = m(x - x_1)$
Step 2 :Plug in the given point $(5, 3)$ and slope $\frac{4}{5}$: $y - 3 = \frac{4}{5}(x - 5)$
Step 3 :Simplify the equation: $y - 3 = \frac{4}{5}x - \frac{20}{5}$
Step 4 :Add 3 to both sides of the equation: $y = \frac{4}{5}x - \frac{20}{5} + 3$
Step 5 :Combine the constants: $y = \frac{4}{5}x - 1$
Step 6 :\(\boxed{y = \frac{4}{5}x - 1}\)