Question

Y = - 2/3x -6
Find the equation of the line that is perpendicular to this line and passes through the point (-3,5) .

Find the equation of the line that is parallel to this line and passes through the point (-3,5)

Answer 1

To find the equation of any linear function (equation of a line) you may use a point and a slope and use y=mx + b

When you are told to find the equation of the line that is "perpendicular" to
y=-2/3 x -6 you are being given a slope (indirectly) of that line.
The slope of our given line is the number in front of x, so m= -2/3

The line that is perpendicular to y has slope -1/m (the negative reciprocal of m)
so -1/m = -1/ (-2/3) = 3/2

so you want to find the equation of the line that has slope 3/2 and goes through the point (-3,5)

Answer 2

so you have Y= Mx + b
Y=3/2 x + b
To find b you plug in the point (-3,5)
5= 3/2 (-3) + b
5= -9/2 +b
5 + 9/2 =b
(10+9)/2=b
19/2=b

Plug this into Y=3/2 x +b
Y=3/2 x + 19/2

Answer 3

For the second question, to find a line that is parallel that means we have the same slope...we want the equation of the line with slope -2/3 and that goes through (-3,5)
Steps are similar to above :-)

Answer 4

Thanks! It's been the better part of a decade since I've done any of this. I know it's hidden away in my brain someplace, just need some reminders.