Write the equation of the line that is perpendicular to the line 2x − 3y = 3 and passes through the point (−8, 2).

y = two thirdsx − 10

y = two thirdsx + 10

y = −three halvesx − 10

y = −three halvesx + 10

Question

Write the equation of the line that is perpendicular to the line 2x − 3y = 3 and passes through the point (−8, 2).

y = two thirdsx − 10

y = two thirdsx + 10

y = −three halvesx − 10

y = −three halvesx + 10

shamil98 · Answer

Can you first change your equation to slope-intercept form? $$\large y = mx + b$$

kainui · Answer

The slope a line that's perpendicular to another line has a slope that is the negative inverse of the other. So if m=slope of the other line, then a perpendicular line is -1/m as the slope. You should check this with some other graphs where you know they're perpendicular. Like y=x and y=-x have slopes of 1 and -1/1 so they're perpendicular. How about a horizontal line? That has a slope of 0, so -1/0 is basically dividing by zero so you have infinity and it rises infinitely without ever running so you go up and never to the right, which is perpendicular. Maybe that's confusing, but play around with some others to make certain I'm not lying to you.

shamil98 · Answer

In summary to what Kainui has explained.
Parallel slopes are equal.
Perpendicular slopes are negative reciprocals (negatively flipped)
perpendicular to 3/4 is -4/3 for example.


To find the equation first change your equation to slope-intercept form and then
plug in your (x,y) coordinates (-8,2) along with your new slope and solve for the b value ( y-intercept).