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

Dec 17, 2016

$y = - \frac{2}{3} x + 2$

#### 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 $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the two points.

Substituting the two points from the problem gives the slope as:

$m = \frac{0 - 2}{3 - 0}$

$m = - \frac{2}{3}$

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: $\textcolor{red}{\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)}$
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:

$y - 0 = - \frac{2}{3} \left(x - 3\right)$

$y = - \frac{2}{3} x + \frac{2}{3} \cdot 3$

$y = - \frac{2}{3} x + 2$