Question

Find the equation of the line passing through the point (-4, 4) and is perpendicular to the line y = 2x - 5.

Answer 1

Answer: y = (-1/2)x + 2

Concept:

When two lines are perpendicular to each other, their slopes are negative reciprocals.

The reciprocal of a number is 1 divided by the number.

In other words, it is the image opposite of a term.

Solve:

Given information

Given line = y = 2x - 5

Point = (-4, 4)

Find the slope of the line

Given the line is perpendicular to the line y = 2x - 5, the slope of the line would be negative reciprocal of the line y = 2x - 5.

Slope of line [y = 2x - 5] = 2

Slope of new line = (-1/2)

Find the y-intercept by substituting the given point

Equation of the new line: y = (-1/2)x + b

• b = y-intercept

y = (-1/2)x + b

4 = (-1/2) (-4) + b

4 = 2 + b

4 - 2 = 2 + b - 2

b = 2

Finalize the equation of the line

Slope = -1/2

Y-intercept = 2

$\boxed{y=-\frac{1}{2}x+2 }$

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