## Write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2, 6).

Question

Write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2, 6).

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3 days 2021-10-10T21:19:50+00:00 1 Answer 0

1. 1. If the line that we are searching for is perpendicular to the line y = -4x, this means that the gradient of our line and the gradient of the perpendicular line will multiply to give -1. Thus if we call the gradient of our line m, then:

m*(-4) = -1

-4m = -1

m = 1/4

2. Since we know that m = 1/4 and we have a point (2,6) on our line, we can use the formula y – y1 = m(x – x1) to find the equation of our line, where (x1, y1) is the coordinates of a point on the line. Thus:

y – y1 = m(x – x1)

y – 6 = (1/4)(x – 2)

y – 6 = (1/4)x – 2/4 (Expand (1/4)(x – 2))

y = (1/4)x – 1/2 + 6 (Simplify 2/4 and add 6 to each side)

y = (1/4)x + 11/2 (Evaluate -1/2 + 6)

Slope-intercept form is given by y = mx + c. As our equation is already in this form, there is nothing more to do. Thus, the answer is y = (1/4)x + 11/2