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A line is perpendicular to y=4x-2 and intersects the point (4,-11). What is the equation of this perpendicular line

User Promise
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2 Answers

4 votes

Answer:

Step-by-step explanation: y=-1/4x-10

User MateuszL
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4.5k points
4 votes

Answer:

The formula of this perpendicular line is y = -1/4x - 10

Explanation:

y=ax+b

where:

a is the slope or gradient of the line.

b is the y-intercept of the line.

x is the independent variable of the function y = f(x).

Line y=4x-2 has a gradient of 4. You can write that as 4/1. It means that when x increases with 1, y will increase by 4. Starting from (0, -2) that means ( {0+1}, {-2+4} ) = (1, 2)

If two lines are perpendicular, then their gradients will multiply together to give -1

So apply this 4/1 * a = -1 so a = - 1/4

now see what we have so far, without doing any algebra yet.

y = -1/4x + b

given this line goes through point (4,-11).

lets find b by substituting x and y.

-11 = -1/4 * 4 + b

b = -11 + 4/4

b = -10

The formula of this perpendicular line is y = -1/4x - 10

User Farsan Rashid
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5.7k points
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