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Question
Write the equation of the line passing through the pair of points (2, 3) and (4, 7) in the form of y = mx + c.
Solution
Let (2, 3) ≡ (x1, y1) and (4, 7) ≡ (x2, y2).
The equation of a line passing through a pair of points is
m = `("y"_2 - "y"_1)/("x"_2 - "x"_1)`
`= (7-3)/(4-2) = 4/2 = 2`
Here, I have two points, which I used to find the slope. Now I need to pick one of the points (it doesn't matter which one), and use it to solve for b
Using the point (2,3), I get :
y = mx + b
3 = 2(2) + b
3 = 4 + b
3 - 4 = b
b = -1
So , y = 2x - 1
On the other hand, if I use the point (4,7), I get:
y = mx + b
7 = 2(4) + b
7 = 8 + b
7 - 8 = b
b = -1
then y = 2x - 1
So it doesn't matter which point I choose. Either way, the answer is the same : y = 2x - 1
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