General form?

Question

Write the equation of the line that passes through the points (-4, 2) and (6, 8) in GENERAL form!

Thanks!

Answer 1

First find the slope.

m = ∆y/∆x = (8 - 2)/(6 - -4) = 6/10 = 3/5

Now plug in a point. Let's choose (6,8).

y - 8 = (3/5)(x - 6)

Multiply by 5 to get rid of fractions.

5y - 40 = 3x - 18
-3x + 5y - 22 = 0

Multiply by -1.

3x - 5y + 22 = 0

Answer 2

First, determine the slope of the line:
The change in y = 8 - 2 = 6
The change in x = 6 - -4 = 10
Thus the slope = 6/10 = 3/5

Using the Point/Slope equation of the line, we get y-8 = (3/5)(x-6)
Distributing we get
y - 8 = (3/5)x - (18/5)
To get to General Form, we'll need to multiply through by 5:
5y - 40 = 3x - 18
Now we move things around to get the General Form: 3x - 5y = -22

Check:
3(-4) - 5(2) = -12 - 10 = -22 (yes!)
3(6) - 5(8) = 18 - 40 = -22 (yes!)

Answer 3

"general form" is y=mx+b.
Just find m with the equation:
m=(change in Y)/(change in X)
Y=mx+b can also be written as
y=m(x-x1)+y1 (where x1 and y1 are any co-ordinates on the line). Just solve these equations.

Answer 4

3x-5y=-22