Question

Given (2,-2), and and y intercept 4, how do you find the equation of the line?

Answer 1

Use the point-slope - see full explanation below:

Explanation:

We have been given two points (the y-intercept is point `(0, 4)`) so we can use the point-slope formula to find the equation for the line.

First, we must find the slope which requires two points:

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 our two points gives:

`m = (color(red)(-2) - color(blue)(4))/(color(red)(2) - color(blue)(0))`

`m = (-6)/2`

`m = -3`

Now, having the slope, we can use it and one of the points to use the point-slope formula to find the equation of the line:

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 our slope and one of the points gives:

`(y - color(red)(4)) = color(blue)(-3)(x - color(red)(0))`

We can also put it into the more familiar slope-intercept form by solving for `y`:

`y - color(red)(4) = color(blue)(-3)x`

`y - color(red)(4) + 4 = color(blue)(-3)x + 4`

`y - 0 = color(blue)(-3)x + 4`

`y = color(blue)(-3)x + 4`