How do you the equation of the line that is perpendicular to the line 2x - 3y = 3 and passes through the point (-8, 2)?

Question

Ethan Adkins · Accepted Answer

When given a line in form #ax-by=c#, the equation of all lines that are perpendicular are of the form:

#bx+ay=k#

Use the given point to find the value of #k# Every perpendicular line has the following equation: #3x+2y=k# To find the value of k, substitute the point #(-8,2)# #3(-8)+2(2)=k# #-24+4=k# #k = -20# The equation of the line perpendicular to #2x - 3y = 3# that passes through the point #(-8,2)# is: #3x+2y=-20#

Savannah Anderson · Answer

undefined To find the equation of the line perpendicular to the given line and passing through the point (-8, 2), we first need to determine the slope of the given line. Then, we find the negative reciprocal of that slope to get the slope of the perpendicular line. Next, we use the point-slope form of the equation of a line to find the equation of the perpendicular line. Finally, we simplify the equation into the desired form, usually slope-intercept or standard form.

Given line: 2x - 3y = 3
Slope of the given line: m = 2/3
Slope of the perpendicular line: Negative reciprocal of 2/3 = -3/2

Using the point-slope form of the equation of a line:
y - y1 = m(x - x1)

Substitute the point (-8, 2) and the slope -3/2 into the equation:
y - 2 = (-3/2)(x - (-8))

Simplify:
y - 2 = (-3/2)(x + 8)

Expand and simplify:
y - 2 = (-3/2)x - 12
y = (-3/2)x - 12 + 2
y = (-3/2)x - 10

Therefore, the equation of the line perpendicular to 2x - 3y = 3 and passing through the point (-8, 2) is y = (-3/2)x - 10.