At what point does the line containing the points $(1, 7)$ and $(3, 11)$ intersect the $y$-axis? Express your answer as an ordered pair.
So first we need to find the slope of the line between the points $(1,7)$ and $(3,11)$. That's easy. The slope is $\frac{11-7}{3-1}=\frac{4}{2}=2$. Now we need to find the equation of the line. We can use point-slope form for that. The equation of the line is $y-7=2(x-1)$. Now let's put it in slope-intercept form, so we can easily find the $x$-intercept. That means we need to solve for $y$. So we get $y=2x+5$. Now we just need to substitute $x=0$ to find the $y$-intercept. So $y=2\cdot 0+5=5$. The point at which the line intersects the $y$-axis is $(0,5)$.

