Nayeli’s Algebra Test

Question

Write the equation for the line that passes through the given point and is perpendicular to the given line.

Point: (1,1)

Line: y = 1/4x -9

Answer 1

Hello!

To find a perpendicular line, you need to find the negative reciprocal of the line's slope.

For the line y = 1/4x - 9, the slope is the fraction before the x (1/4).

The negative reciprocal of 1/4 is -4; therefore, the slope for the perpendicular line is -4.

Use the formula y= mx +b to find the perpendicular line, with y and x being the point the line passes through (1, 1).

y = mx + b

1 = 1(-4) + b

1 = -4 + b

(add 4 to both sides to find the value of b)

5 = b

Substitute the value for b in the formula with the negative reciprocal slope:

y = -4x + 5

Answer 2

Perpendicular lines have slopes that are negative reciprocals of one another.

The line that was given has a slope of 1/4, the negative reciprocal of that is -4.

Therefore the equation that is perpendicular to the given line has a slope of -4.

Plug the point into the equation

Y=ax+b

1=-4 (1)+b

b=5

The equation should be Y= -4x+5