# How do you find the equation of a line in slope intercept form given the x intercept 2 and y intercept 3?

Jun 2, 2016

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

graph{y=-3/2x+3 [-10, 10, -5, 5]}

#### Explanation:

A line is straight, meaning the gradient/slope is never changing or constant. So, if we know the line passes through (0,3) and (2,0), then if we draw and straight line connecting the 2 points we'll get the graph.

To solve algebraically, we must understand that the gradient of a line is rise over run, $\frac{r i s e}{r u n}$. in order to find $\frac{r i s e}{r u n}$, we must know two points which it runs through, which we have, (0,3) and (2,0).

Now to find rise, we find out how much the line drops or rises between the two points. Between the two points, we see the line has moved -3 points. It is negative as it has dropped.

Now finding run, we find out how much the line moves horizontally. We see that it has moved 2 points between the 2 points.

Now that we have find rise and run, by placing it into the $\frac{r i s e}{r u n}$ equation, we can find the gradient, which is $- \frac{3}{2}$.

Now the final part is to find the y-intercept. the y-intercept is when x=0 or when the line crosses over the y axis. This cross over is at (3,0), which was given to us as a point.

Now we combine these values to get the equation in intercept form.

$y = m x + c$

(where m is gradient and c is the y-intercept )