Line L is tangent to y=5x^2+8x and parallel to 12x+y=4. What is the y-intercept of line L?

Answer 1

If 12x + y = 4, then y = -12x + 4. So, since parallel lines have the same slope, line L has slope -12.

Since line L is tangent to the curve y = 5x² + 8x, y' = -12 at the point of tangency.

So, 10x + 8 = -12 Therefore, the curve and line L intersect at the point (-2, 4)

Equation of line L is y - 4 = -12(x + 2). So, y = -12x - 20.

Line L has y-intercept (0, -20). .