What is the $y$-coordinate of the $y$-intercept of the line that passes through the point $(2,-3)$ and has slope $\frac12$?
I need to find the equation of the line that passes through $(2,-3)$ and has slope $\frac12$. I can use the point-slope form of a line, which is $y-y_1=m(x-x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Plugging in the given values, I get $y-(-3)=\frac12(x-2)$. Simplifying, I get $y+3=\frac12x-1$. Subtracting $3$ from both sides, I get $y=\frac12x-4$. This is the equation of the line in slope-intercept form, where the $y$-intercept is the constant term. Therefore, the $y$-coordinate of the $y$-intercept is $-4$. 