9. What is an equation of the line that passes through the points (-6,-3) and (-2,3)

To find the equation of the line that passes through the points $(-6,-3)$ and $(-2,3)$, we can use the slope-intercept form of a linear equation, which is $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.<br /><br />Step 1: Calculate the slope of the line using the formula:<br />\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]<br />where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.<br /><br />Substituting the given points $(-6,-3)$ and $(-2,3)$ into the formula, we get:<br />\[ m = \frac{3 - (-3)}{-2 - (-6)} = \frac{6}{4} = \frac{3}{2} \]<br /><br />Step 2: Use the slope-intercept form of a linear equation to find the equation of the line.<br /><br />We know that the slope $m = \frac{3}{2}$ and we can use one of the given points to find the y-intercept $b$. Let's use the point $(-6,-3)$.<br /><br />Substituting the values of $m$ and the coordinates of the point $(-6,-3)$ into the equation $y = mx + b$, we get:<br />\[ -3 = \frac{3}{2}(-6) + b \]<br />\[ -3 = -9 + b \]<br />\[ b = 6 \]<br /><br />Step 3: Write the equation of the line using the slope-intercept form.<br /><br />Now that we have the slope $m = \frac{3}{2}$ and the y-intercept $b = 6$, we can write the equation of the line as:<br />\[ y = \frac{3}{2}x + 6 \]<br /><br />Therefore, the equation of the line that passes through the points $(-6,-3)$ and $(-2,3)$ is $y = \frac{3}{2}x + 6$.