How to make a standard form equation from two points
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First, simplify the equation given into slope intercept form.
slope intercept form is y = mx + b, where b is the y intercept and m is the slope.
3x - 2y - 5 = 0
I would move the 2y to the other side.
3x - 5 = 2y
Then, since y can't have a coefficient, divide everything by 2;
y = 3/2x - 5/2
So there's your slope intercept form.
Point slope form is:
Where those with a subscript of 1 are part of the same point.
So you already known one point; -8, 8. I'll just do that as the pair with subscript 1. You know the slope as well from the slope intercept form; 3/2.
You can just plug those in.
y - 8 = 3/2 (x + 8)
Now to change this to general form.
First, distribute 3/2 to x and 8.
y - 8 = 3/2x + 12
-3/2x + y = 20
-3/2x + y - 20 = 0
Since there are no fractions, multiply everything by 2.
-3x + 2y - 40 = 0
slope intercept form is y = mx + b, where b is the y intercept and m is the slope.
3x - 2y - 5 = 0
I would move the 2y to the other side.
3x - 5 = 2y
Then, since y can't have a coefficient, divide everything by 2;
y = 3/2x - 5/2
So there's your slope intercept form.
Point slope form is:
Where those with a subscript of 1 are part of the same point.
So you already known one point; -8, 8. I'll just do that as the pair with subscript 1. You know the slope as well from the slope intercept form; 3/2.
You can just plug those in.
y - 8 = 3/2 (x + 8)
Now to change this to general form.
First, distribute 3/2 to x and 8.
y - 8 = 3/2x + 12
-3/2x + y = 20
-3/2x + y - 20 = 0
Since there are no fractions, multiply everything by 2.
-3x + 2y - 40 = 0