(5,9) and (3,-1) y=5x-16 ) y=-5x+16 y=1/5x-16 y=-1/5x+16

To find the equation of the line passing through the points $(5,9)$ and $(3,-1)$, we can use the slope-intercept form of a linear equation: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.<br /><br />Step 1: Calculate the slope using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$.<br /> $m = \frac{-1 - 9}{3 - 5} = \frac{-10}{-2} = 5$<br /><br />Step 2: Use one of the given points to find the y-intercept. Let's use $(5,9)$.<br /> $9 = 5(5) + b$<br /> $9 = 25 + b$<br /> $b = 9 - 25$<br /> $b = -16$<br /><br />Step 3: Write the equation of the line using the slope-intercept form.<br /> $y = 5x - 16$<br /><br />Therefore, the equation of the line passing through the points $(5,9)$ and $(3,-1)$ is $y = 5x - 16$.