Wondering if I did this right?

Question

Write a general linear equation that passes through (-2,1) and (2,-2). I ended up with 8y+3x=-1. Can anyone let me know if this is correct? And if it's not, explain?

Answer 1

Use the equation: y - y1 = [(y2-y1)/(x2-x1)](x-x1) to find a linear equation with (-2,1) and (2,-2) as solutions.

y - 1 = [(-2-1)/(2+2)](x-2)

Simplify:

y-1 = (-3/4)(x-2)

y = (-3/4)x - (3/2) + 1

y = (-3/4)x - 1/2   <-- slope-intercept form

4y = -3x - 2

3x + 4y = -2   <-- standard form

3x + 4y + 2 = 0 <-- general form

Answer 2

It can't be right.  Take your first point and plug it in:

8(1) + 3(-2) = 8 + (-6) = -2, which is not the same as -1.

Fine the slope:  m = (y2 - y1)/(x2 - x1) = (1 - (-2))/(-2 - 2) = 3/-4 = -3/4

Now use the point-slope form:

y - y1 = m(x - x1)  (it makes no difference which point you use)

y - 1 = (-3/4)(x + 2)

4y - 4 = -3x - 6

3x + 4y = -2

Check it by plugging in each point.  If we did it right, both should work.