Question

What is the equation of the line that passes through (–2, –3) and is perpendicular to 2x – 3y = 6?

Answer 1

first we need to find the slope of 2x - 3y = 6. The reason we have to do this is because perpendicular lines have negative reciprocal slopes. Do you know how to find the slope of that line ?

Answer 2

I think the slope is 2?
right?

Answer 3

2x - 3y = 6 -- subtract 2x from both sides
-3y = -2x + 6 -- divide by -3
y = 2/3x - 2
In y = mx + b form, the slope is in the m position...therefore the slope is 2/3.
However, we need the negative reciprocal slope. All that means is " flip " the slope and change the sign. So the slope we need, the negative reciprocal, is -3/2.
Do you understand so far ?

Answer 4

do you have any questions or shall I continue ?

Answer 5

Continue please

Answer 6

now we will use y = mx + b
slope(m) = -3/2
(-2,-3)...x = -2 and y = -3
we already found the slope we will be using, so all we need to do is find the y intercept (b)
now sub and find b, the y intercept
y = mx + b
-3 = -3/2(-2) + b
-3 = 3 + b --- subtract b from both sides
-3 - 3 = b
-6 = b

so our perpendicular equation is : y = -3/2x - 6
any questions ?

Answer 7

no thanks bro

Answer 8

oops..typo...I meant subtract 3 from both sides...not b...lol