Question

How do you write an equation with X-intercept of 3 and y-intercept of 2?

Answer 1

`y = -2/3x + 2`

Explanation:

By definition the x-intercept of 3 is the point (3, 0) and

By definition the y-intercept of 2 is the point (0, 2).

Because we have two points we can use the point-slope formula to determine the equation. In order to use the point-slope formula we must first determine the slope of the line.

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 the two points from the problem gives the slope as:

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

`m = -2/3`

Now that we have the slope we can use the point-slope formula to determine the equation of the line:

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.

We can substitute the slope we calculated and one of the points to give:

`y - 0 = -2/3(x - 3)`

`y = -2/3x + 2/3 * 3`

`y = -2/3x + 2`