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.

Answer 1

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