Determine the equation of the line perpendicular to y = 1/4x + 1 that passes through (-4,7).

Answer 1

The slope of the given line is 1/4 (the equation is given in slope-intercept form y = mx + b).

Any line perpendicular to the given line has a slope that is the negative reciprocal of 1/4 (which is -4, because 1/4 (-4) = -1).

Now you have a choice to use point-slope or slope-intercept to write the equation of the line with slope -4 and passing through the point (-4, 7).

Point-Slope (y - y₁) = m(x - x₁)

y - 7 = -4(x - [-4])

y - 7 = -4(x + 4)

y - 7 = -4x - 16

y = -4x - 9

Point-Slope y = mx + b (when x = -4, y = 7)

7 = -4(-4) + b

7 = 16 + b

b = -9

y = -4x - 9

This Desmos graph confirms and also shows you how to access the coordinates of a named point:

desmos.com/calculator/econlg3eie