Lesson Finding the equation of a line given two points (standard form)

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Problem: Find the equation of the straight line through (-6,-3) and (3.5,-6)
Record the answer in Ax+By = C form, aka standard form.

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Solution:

Compute the slope of the line through (-6,-3) and (3.5,-6)
m = slope
m = rise/run
m = (y2 - y1)/(x2 - x1)
m = (-6-(-3))/(3.5-(-6))
m = (-6+3)/(3.5+6)
m = (-3)/(9.5)
Notice how I'm not fully computing the slope value to get a single number, but rather leaving it in this ratio form.

Use the slope ratio to determine the coefficients A and B
m = -A/B
(-3)/(9.5) = -A/B
A = 3, B = 9.5
Technically infinitely many answers are possible for this A,B pairing; however, it's easiest to stick with the rise,run values.

So,
Ax+By = C
becomes
3x+9.5y = C

Then plug in the coordinates of one of the points. 
Let's say we plugged in (x,y) = (-6,-3)
3x+9.5y = C
3(-6)+9.5(-3) = C
-46.5 = C
C = -46.5

We have: A = 3, B = 9.5, C = -46.5
We go from Ax+By = C to 3x+9.5y = -46.5

Then multiply both sides by 2 to clear out the decimals
3x+9.5y = -46.5
2*(3x+9.5y) = 2*(-46.5)
6x+19y = -93

Answer: <font color=red>6x+19y = -93</font>