A line is perpendicular to y=-4x-2 and intersects the point (0,9). What is the equation of this perpendicular line?

Answer 1

Answer: y = 1/4(x) + 9

Equation of a linear line: y = mx+b, where m is the slope and b is the y-intercept. When two lines are perpendicular, their slopes are negative reciprocals of each other. The equation of the line y = -4x-2 has a slope of -4, so the line perpendicular to this line has a slope 1/4.

We now know m, and need to find b of the equation of the perpendicular line. The intersection point between the two points is (0,9), so we can plug in x as 0 and y as 9 into the equation y = 1/4(x) + b. When we do that, we get 9 = 1/4(0) + b, and when we simplify, we get b = 9. Therefore, the equation of the line perpendicular to y = -4x-2 is y = 1/4(x) +9

Answer 2

Hi Bailey

y= (1/4)x + 9

In Slope Intercept Form y = mx + b, you are given the line

y = -4x-2

Where m = -4

The perpendicular line would have an inverse slope of the opposite sign, the inverse of -4 with the opposite sign is

m = 1/4

You are also given that the perpendicular line passes through the point (0, 9), in Slope Intercept Form

y = mx + b, when x = 0, y = b so b is 9.

I hope this helps.

You can graph both lines on paper, with a graphing calculator or at Desmos.com to confirm that they are perpendicular.