maths problem?

Question

find the equation of the line through the point (1, -6) and which is parallel to the line 3x + 2y - 4 = 0


i cant get this. i found out the slope of 3x + 2y - 4 = 0 which is -3. so the slope of this line must be that.
but when i try to verify if (1, -6) is on the line, i don't get an answer of 0, i get 13.

could anyone help me out? thanks

Answer 1

Sure.

3x + 2y - 4 = 0
2y = -3x + 4
y = (-1.5)x + 2

So the slope of the line isn't -3, it's -1.5 :)

So the equation is (in slope-intercept form)

y = mx+b, where m = -1.5 and b is something
y = -1.5x + b

Plug in the point (1, -6) for x and y.

-6 = -1.5(1) + b
-6 = -1.5 + b
b = -4.5

So the equation is y = -1.5x - 4.5

Answer 2

Let's call the line through point (1,-6) line A. You are told that line A is parallel to the line 3x+2y-4=0 which we will call line B. That means that the gradient of line A is the same as that line B.

You need to find the gradient of line B and that means rearranging 3x+2y-4 into the form y=mx+c which is the equation of a straight line where m is the gradient and c is the intercept on the y axis. So:

3x+2y-4=0

2y = 4 - 3x

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

Hence the gradient of line B and also of line A is -3/2.

Now consider just line A. You know it has gradient
m = -3/2 and passes through the point x = 1 and y = -6.

Using m = (y2 - y1)/(x2-x1) you get:

-3/2 = (-6 - y)/(1-x)

-3/2(1-x) = (-6 -y)

Multiply both sides by -2 gives

3(1-x) = -2(-6-y)

3 - 3x = 12 +2y

2y = 3 - 3x -12

2y = -9-3x

y = (-9/2) -3x/2

y = -3x/2 - 9/2

Note that point (1,-6) is NOT on line B. I think that is where you have been going wrong. Hope this has helped.

Answer 3

The reason you don't get an answer of 0 is because (1,-6) isn't meant to be on that line, but on one parallel to it. The slope is the same, but other wise that's it. Given the slope and a point that it goes through you should be able to work out the equation, as I think someone above has already done for you.

Answer 4

What he said? Haha I'm doing As level maths and im stuck on that