Question

Write the equation of the line that passes through (–2, 1) and is perpendicular to the line 3x – 2y = 5.

Answer 1

first we need to find the slope in the equation 3x - 2y = 5. Do you know how to do that ?

Answer 2

put the equation in y = mx + b form, and m will be the slope

Answer 3

it would be y= 3/2x-5/2 right?

Answer 4

3x - 2y = 5
-2y = -3x + 5
y = 3/2x - 5/2
yes...the slope is 3/2, but we need a perpendicular line, therefore, we need the negative reciprocal of that slope. All that means is " flip " the slope and change the sign. Therefore, the slope we need to use is -2/3. Do you see how I flipped the slope and changed the sign ? Do you understand so far ?

Answer 5

yepp

Answer 6

now we can use either y = mx + b form or y - y1 = m(x - x1) form...you will arrive at the same answer either one you choose to use. Which formula do you want to use ?

Answer 7

or I can show you how to use both ....do you want me to show you both ?

Answer 8

y-y1=m(x-x1)

Answer 9

y - y1 = m(x - x1)
slope(m) = -2/3
(-2,1) x1 = -2 and y1 = 1
now we sub
y - 1 = -2/3(x - (-2)
y - 1 = -2/3(x + 2)
y - 1 = -2/3x - 4/3
y = -2/3x - 4/3 + 1
y = -2/3x - 4/3 + 3/3
y = -2/3x - 1/3 <-- your perpendicular line

any questions ?

Answer 10

No. Thank you !

Answer 11

you could have also done this.. y = mx + b and find b
slope(m) = -2/3
(-2,1) x = -2 and y = 1
now we sub
y = mx + b
1 = -2/3(-2) + b
1 = 4/3 + b
1 - 4/3 = b
3/3 - 4/3 = b
-1/3 = b
leaving you with y = -2/3x - 1/3

Answer 12

Thanks

Answer 13

anytime :)