J) A A line passes through the points (-6,10) and (9,0) . Write its equation in slope-intercept form. Write your answer using integers , proper fractions, and improper fractions in simplest form. square

To find the equation of a line in slope-intercept form, we need to determine the slope and the y-intercept.<br /><br />Step 1: Find the slope (m) using the formula:<br />\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \]<br /><br />Given points: $(-6,10)$ and $(9,0)$<br />\[ m = \frac{{0 - 10}}{{9 - (-6)}} = \frac{{-10}}{{15}} = -\frac{2}{3} \]<br /><br />Step 2: Use the slope-intercept form equation:<br />\[ y = mx + b \]<br /><br />Substitute the slope and one of the given points into the equation to solve for the y-intercept (b):<br />\[ 10 = -\frac{2}{3}(-6) + b \]<br />\[ 10 = 4 + b \]<br />\[ b = 6 \]<br /><br />Step 3: Write the equation of the line in slope-intercept form:<br />\[ y = -\frac{2}{3}x + 6 \]<br /><br />Therefore, the equation of the line passing through the points $(-6,10)$ and $(9,0)$ is:<br />\[ y = -\frac{2}{3}x + 6 \]