Question

Which equation represents the line that is perpendicular to and passes through (-40,20)?

a. y=2x+60
b. y=−0.5x+40
c. y=x+20
d. y=−x+60

Answer 1

The equation of the line that is perpendicular to and passes through (-40,20) is y = -1/2x + 20.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The line perpendicular to the given line will have a slope of -1/2. To find the equation of the line, we can use the point-slope form of a line, y - y1 = m(x - x1). Substituting the given point (-40,20) and the slope (-1/2) into the equation, we get y - 20 = (-1/2)(x - (-40)).

Simplifying the equation, we get y - 20 = (-1/2)(x + 40). Distributing the -1/2, we get y - 20 = -1/2x - 20. Rearranging the equation to the slope-intercept form, we get y = -1/2x + 0. Adding 20 to both sides, we get y = -1/2x + 20.