# 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 $$m=\frac{rise}{run}$$ Nov 24, 2016 at 14:01

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 $m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-0}{0-8}=-\frac{11}{8}$