Question

What is the line containing the points (0, 4) and (3, -2)?

Answer 1

`y - 4 = -2x` or `y = -2x + 4`

Explanation:

To find the line containing these two points we must first determine the slope.

The slope can be found by using the formula: `color(red)(m = (y_2 = y_1)/(x_2 - x_1)`
Where `m` is the slope and `(x_1, y_1)` and `(x_2, y_2)` are the two points.

Substituting our two points gives:

`m = (-2 - 4)/(3 - 0)`

`m = (-6)/3`

`m = -2`

Next we can use the point-slope formula to find the equation for the line passing through the two points.

The point-slope formula states: `color(red)((y - y_1) = m(x - x_1))`
Where `m` is the slope and #(x_1, y_1) is a point the line passes through.

Substituting `-2` for `m` and (0, 4) for the point gives:

`y - 4 = -2(x - 0)`

`y - 4 = -2x`

Now, solving for `y` to put the equation in the slope-intercept format gives:

`y - 4 + 4 = -2x + 4`

`y - 0 = -2x + 4`

`y = -2x + 4`