10. What is an equation of the line that passes through the points (-1,2) and (-2,-1)

To find the equation of the line that passes through the points $(-1,2)$ and $(-2,-1)$, we can use the slope-intercept form of a linear equation, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.<br /><br />Step 1: Calculate the slope ($m$) 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 given points.<br /><br />Substituting the values of the points $(-1,2)$ and $(-2,-1)$ into the formula, we get:<br />\[ m = \frac{-1 - 2}{-2 - (-1)} = \frac{-3}{-1} = 3 \]<br /><br />Step 2: Use the slope-intercept form of a linear equation to find the equation of the line.<br />\[ y = mx + b \]<br />Substituting the value of the slope ($m = 3$) and one of the given points ($(-1,2)$) into the equation, we get:<br />\[ 2 = 3(-1) + b \]<br />\[ 2 = -3 + b \]<br />\[ b = 5 \]<br /><br />Step 3: Write the equation of the line using the slope-intercept form.<br />\[ y = 3x + 5 \]<br /><br />Therefore, the equation of the line that passes through the points $(-1,2)$ and $(-2,-1)$ is $y = 3x + 5$.