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Line L, given by the graph of y = 5x + 6, intersects the graph of y = x² at two points P = (a, b) and Q = (c,d), such that a < c. What is the y-intercept of the line perpendicular to L passing through P?

 Aug 12, 2023
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Since line L intersects the graph of y = x² at two points, then the x-coordinate of each point must satisfy y = 5x + 6 = x². Solving this equation for x, we get x = 1 or x = -6.

Therefore, the points of intersection are P = (1, 11) and Q = (-6, 16).

The slope of L is 5, and since the two lines are perpendicular, the slope of the line perpendicular to L passing through P is -1/5.

Using the point-slope form of linear equations, the equation of the perpendicular line passing through P is y - 11 = -1/5(x - 1). Solving for y, we get y = -1/5*x + 16/5.

The y-intercept of this line is 16/5, so the answer is 16/5.

 Aug 12, 2023

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