8. What is an equation of the line that passes through the points (2,6) and (1,3)

To find the equation of the line that passes through the points $(2,6)$ and $(1,3)$, 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 given points.<br /><br />Substituting the values of the given points:<br />\[ m = \frac{3 - 6}{1 - 2} = \frac{-3}{-1} = 3 \]<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 $m = 3$:<br />\[ y = 3x + b \]<br /><br />Step 3: Substitute one of the given points into the equation to solve for the y-intercept $b$.<br />Let's use the point $(2,6)$:<br />\[ 6 = 3(2) + b \]<br />\[ 6 = 6 + b \]<br />\[ b = 0 \]<br /><br />Step 4: Write the final equation of the line using the slope and y-intercept.<br />\[ y = 3x + 0 \]<br />\[ y = 3x \]<br /><br />Therefore, the equation of the line that passes through the points $(2,6)$ and $(1,3)$ is $y = 3x$.