how do I determine which equation represents the line that is perpendicular to
y=4/5x+23 and passes through (-40,20)?
A. y=-5/4x-15
B. y=-5/4x-30
C. y=4/5x+52
D. y=4/5x-56
To determine which equation represents the line that is perpendicular to y=4/5x+23 and passes through (-40,20), we need to find the negative reciprocal of the slope of the given line, and then use this slope and the given point (-40,20) to find the equation of the line using the point-slope form.
The equation y=4/5x+23 is already in slope-intercept form (y = mx + b) where the slope (m) is 4/5. The negative reciprocal of this slope is -5/4.
Using the point-slope form, y - y1 = m(x - x1), we can substitute the values of (-40, 20) and the negative reciprocal slope (-5/4) into the equation:
y - 20 = -5/4(x - (-40))
y - 20 = -5/4(x + 40)
y - 20 = -5/4x + 200/4
y - 20 = -5/4x + 50
y = -5/4x + 70
So the equation that represents the line that is perpendicular to y=4/5x+23 and passes through (-40,20) is y = -5/4x + 70.
The correct answer is A. y = -5/4x - 15.