Question

What is the equation in point-slope form of the line passing through (0, 2) and (1, 5)?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the slope of the line. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(5) - color(blue)(2))/(color(red)(1) - color(blue)(0)) = 3/1 = 3`

The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Substituting the slope we calculated and the values from the first point in the problem gives:

`(y - color(red)(2)) = color(blue)(3)(x - color(red)(0))`

Or

`(y - color(red)(2)) = color(blue)(3)x`

We can also substitute the slope we calculated and the values from the second point in the problem giving:

`(y - color(red)(5)) = color(blue)(3)(x - color(red)(1))`