Test 5 Section 2 - #17 (page 642)

It's important to note that when the SAT tells you that a line passes through the origin, they're giving you a point on the line: (0,0). So we know line l contains points (0,0) and (t, t+1).

Since we also know that it's perpendicular to the line y = -4x + k, we know line l has a slope of +1/4 (the negative reciprocal of the slope of the line it's perpendicular to).

We can use these two facts to solve for t. Set up the slope equation using the points we know:

1/4 = [t + 1 -0]/[t - 0]

1/4 = [t + 1]/[t]

t/4 = t + 1

t = 4t + 4

-3t = 4

t = -4/3