Question

I am trying to work through the following equations and can't remember how to do them. I would appreciate if someone could show me how to do both questions so I can see the difference.

Find the equation of the line that passes through
A(4,-2) and is parallel to 2x-3y=7
A(-2,5) and is perpendicular to 2x-y=6

Answer 1

You should try these your self. There are three steps. Do them both the same way.

Put the equation of the line that you want to be parallel to in the form
y = mx + b
That tells you the slope, m.

For the first equation y = (2/3)x -7/3. Therefore the slope is m = 2/3 for that line.

For the second step, write this equation for a line going through the point (x*, y*):

y - y* = m(x - x*)
I find this form very easy to remember. It is easy to see why y must equal y* when x = x*, forcing the line to go through the point.

Then, if you want, rearrange the equation into standard y = mx + b form.

y = mx + (y*-mx*)

Answer 2

Thanks for the help. I tried to work is out and came up with this working out:
A(4,-2) is parallel to 2x-3y=7

y = mx + c
-3y = -2x + 7
y = 2/3x - 2 1/3

(y-y*) / (x-x*) = m
(y+2) / (x-4) = 2/3
y+2 = 2/3(x-4)
y+2 = 2/3x - 2 2/3
y = 2/3x-2 2/3 - 2
y = 2/3x-4 2/3

Answer 3

That is the correct answer. Good work! Now do the other one