[tex]\huge\boxed{(0, 23)}[/tex]
Hey there! We'll solve this problem in three main steps. First, we'll find the slope of the line. Then, we'll find the equation line in point-slope form. Finally, we'll change the equation to slope-intercept form so we can tell what the y-intercept is.
We can use the slope formula, where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two known points on the line.
[tex]\begin{aligned}m&=\frac{y_2-y_1}{x_2-x_1}&&\smash{\Big|}&&\text{Use the slope formula.}\\&=\frac{-10-1}{3-2}&&\smash{\Big|}&&\text{Substitute in the known values.}\\&=\frac{-11}{1}&&\smash{\Big|}&&\text{Subtract.}\\&=\boxed{-11}&&\smash{\Big|}&&\frac{x}{1}=x\end{aligned}[/tex]
Now that we have the slope, we can use it together with one of the points to get the line in point-slope form. Then, we can distribute and add to get the line in slope-intercept form.
[tex]\begin{aligned}y-y_1&=m(x-x_1)&&\smash{\Big|}&&\text{Use point-slope form.}\\y-1&=-11(x-2)&&\smash{\Big|}&&\text{Substitute in the slope and one point.}\\y-1&=-11x+22&&\smash{\Big|}&&\text{Distribute.}\\y&=-11x+\boxed{23}&&\smash{\Big|}&&\text{Add $1$ to both sides.}\end{aligned}[/tex]
We can now clearly see that the y-intercept of the line is [tex]23[/tex], or [tex](0, \boxed{23})[/tex] as a point.
