Answer
$y$-intercept $=-3$
Work Step by Step
Point on a line: $(2,-6)$ $;$ Line's slope: $-\dfrac{3}{2}$
Obtain the $y$-intercept. Do so by obtaining the line's equation first.
The point-slope form of the equation of a line is $y-y_{1}=m(x-x_{1})$, where $m$ is the slope of the line and $(x_{1},y_{1})$ is a point through which it passes.
Both $m$ and $(x_{1},y_{1})$ are given, so substitute them into the point-slope form of the equation of a line formula and simplify:
$y-y_{1}=m(x-x_{1})$
$y-(-6)=-\dfrac{3}{2}(x-2)$
$y+6=-\dfrac{3}{2}x+3$
Solve for $y$:
$y=-\dfrac{3}{2}x+3-6$
$y=-\dfrac{3}{2}x-3$
The equation is now in slope-intercept form and according to that form, which is $y=mx+b$, $b$ is the $y$-intercept of the line.
In this case, it can be seen that $b=-3$, so the $y$-intercept of the line is $(0,-3)$
