A line is drawn through the points $(-2, 6)$ and $(-4, -2)$. What is the $y$-coordinate of the point where this line intersects the $y$-axis?
I need to find the equation of the line that passes through $(-2, 6)$ and $(-4, -2)$. To do that, I can use the slope-intercept form of a line, $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. First, I need to find the slope $m$ of the line. The slope is the change in $y$ over the change in $x$ between two points on the line. So, the slope is $\frac{-2 - 6}{-4 - (-2)} = \frac{-8}{-2} = 4$. Now that I have the slope, I can plug in one of the points, say $(-2, 6)$, into the equation $y = mx + b$ and solve for $b$. I get $6 = 4(-2) + b$, which simplifies to $6 = -8 + b$, so $b = 14$. This means the equation of the line is $y = 4x + 14$. To find the $y$-coordinate of the point where the line intersects the $y$-axis, I need to set $x = 0$ and solve for $y$. I get $y = 4(0) + 14$, which simplifies to $y = 14$.

