What is the equation of a line that is perpendicular to y = 4x + 5 and passes through point (8, 3)?

Solution:

The equation y = 4x + 5 in the form y = mx + c.

The slope of the line is 4.

If the slope of one line is m₁ and if the slope of the line perpendicular to it is m₂ then:

m₁m₂ = -1

Since the slope of y = 4x + 5 is 4 then the line perpendicular to it will have a slope of -1/4

Hence the equation of the line perpendicular to y = 4x + 5 will be

y = (-1/4)x + c

4y = -x + 4c

The perpendicular line passes through point (8,3).

Therefore the value of c can be calculated as:

4c = x + 4y

4c = 8 + 4(3)

4c = 8 + 12

4c = 20

c = 5

Therefore the equation of the line perpendicular to y = 4x + 5 is:

4y = - x + 4(5)

4y = -x + 20

y = -x/4 + 5

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What is the equation of a line that is perpendicular to y = 4x + 5 and passes through point (8, 3)?

Summary:

The equation of a line that is perpendicular to y = 4x + 5 and passes through point (8, 3) is y = -x/4 + 5