Question

What is the equation of the line that passes through (2, 4) and (4, 10)?

Answer 1

`y = 3x - 2`

Explanation:

The equation of the line that passes through two points

`(x_1, y_1)` and
`(x_2, y_2)` is

`y - y_1 = (y_2 - y_1)/(x_2 - x_1)(x - x_1)`

We have points (2, 4) and (4, 10), so we have

`x_1 = 2`

`y_1 = 4`

`x_2 = 4`

`y_2 = 10`

Now we plug in those values into the equation above, simplify, and solve for y.

`y - 4 = (10 - 4)/(4 - 2)(x - 2)`

`y - 4 = (6)/(2)(x - 2)`

`y - 4 = 3(x - 2)`

`y - 4 = 3x - 6`

`y = 3x - 2`