Question

Find the slope of the line passing through the points (4,-2) and (-1,1) and put the equation in standard form. (Ax + By = C)

Please show all your work so i can do the next one myself.

Answer 1

Find the slope.
http://www.coolmath.com/algebra/08-lines/06-finding-slope-line-given-two-points-01.htm

Answer 2

Slope = (y2-y1) / (x2-x1)

Answer 3

Once you know the slope m, (y-y1) = m(x-x1) is the equation of the line.
You can rearrange the terms to put it in standard form.

Answer 4

The points are (4,-2) and (-1,1)
Slope m = (y2-y1) / (x2-x1) = (1 - (-2)) / (-1 - 4) = (1+2)/(-5) = -3/5
Knowing the slope m and any point on the line (either (4,-2) or (-1,1)) we can find the equation of the line. We will choose the (-1,1) point because it is simpler than (4,-2):
y - y1 = m(x - x1)
y - 1 = -3/5(x - (-1)) = -3/5(x + 1)
y - 1 = -3/5x - 3/5
y = -3/5x - 3/5 + 1
y = -3/5x + 2/5
multiply throughout by 5
5y = -3x + 2
add 3x to both sides:
3x + 5y = 2 is the equation of the line in standard form.

Answer 5

After find the equation, it is a good idea to put the points back and see if they satisfy the equation. I tried both (4, -2) and (-1, 1) in 3x + 5y = 2 and both satisfy the equations.