What is the slope of a line that has an

What is the slope of a line that has an X-Intercept of 8 and a Y-Intercept of 11?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

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 $\left(8,0\right)$ and $\left(0,11\right)$ are points on this line. Therefore, the slope of the line is $\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}$, 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 $y-{y}_{1}=m\left(x-{x}_{1}\right)$) 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 $\left(8,0\right)$, although we can very easily choose the other point and get the same formula, so that the formula for this line is $y-0=\frac{-11}{8}\left(x-8\right)\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}y=\frac{-11}{8}x+11$
Did you like this example?
gnatopoditw
The intercepts can be treated as special points. In your case you have $\left(8,0\right)$ and $\left(0,11\right)$.
$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}=\frac{11-0}{0-8}=-\frac{11}{8}$