Question 769932: What does the y in y=mx+b mean/stand for? And it says it works for any coordinate pair but how come when a line passes through (1,6) and (-3,5) using (1,6) y=10 but using (-3,5) its -7?
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Work out the gradient first.
The gradient is the slope or 'm'
y2 - y1/x2 - x1 (1,6) (-3,5)
5 - 6/-3 - 1 = 1/4
Next using the equation:
y - b = m(x - a)
a and b are x and y from either
of your coordinates. (1,6) (-3,5)
I will use (1,6)
So, a = 1, b = 6 and m = 1/4
y - b = m(x - a)
y - 6 = 1/4(x - 1)
y - 6 = 1/4x - 1/4
y = 1/4x - 1/4 + 24/4 (+6)
y = 1/4x + 23/4
Or multiply thro by 4 to remove fractions.
4y = x + 23
................
Now using (1,6)
4(6) = 1 + 23
24 = 24
Using (-3,5)
4(5) = -3 + 23
20 = 20
Hope this helps.
:-)
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