# Find slope using X-Intercept and Y-intercept

My mathematics teacher explained how to find slope using 2 different points but I was never taught how to use the X-Intercept and the Y-Intercept to find the slope.

Example question: What is the slope of a line that has an X-Intercept of 8 and a Y-Intercept of 11?

• What are the coordinates of the x-intercept? the y-intercept? Try plotting them on a graph ... the answer should be obvious.. Remember $$m=\frac{rise}{run}$$ – John Joy Nov 24 '16 at 14:01

## 2 Answers

If we know the X-Intercept and the Y-Intercept, then we have two points. With two points, we can define the slope of the line and, indeed, an equation for the line through those two points.

Using your example, suppose the X-Intercept is 8 and Y-Intercept is 11. Then we know that $(8,0)$ and $(0,11)$ are points on this line. Therefore, the slope of the line is $\frac {\Delta y}{\Delta x}$, or the change in $y$ over the change in $x$. Therefore, $slope=\frac {0-11}{8-0}=\frac{-11}{8}$. Now we can use point-slope form for a line through a point to give a formula for the line.

Point-slope form is defined by $y-y_1=m(x-x_1)$ where $x_1,y_1$ are the $x$ and $y$ values from one of your points, and $m$ is the slope. I will use the point $(8,0)$, although we can very easily choose the other point and get the same formula, so that the formula for this line is $y-0=\frac{-11}{8}(x-8) \implies y=\frac{-11}{8}x+11$

The intercepts can be treated as special points. In your case you have $(8,0)$ and $(0,11)$.

You can get the gradient from that by using gradient $m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-0}{0-8}=-\frac{11}{8}$

• "Gradient". I like that. I, Sir Jony, hereby declare that everyone use the term "gradient" rather than "slope". :) – Fine Man Nov 23 '16 at 7:03