Question

what is the slope of this line?

Explanation:

Step1: Select two points

Let's take two points on the line, say $(0, 1)$ and $(5, 6)$.

Step2: Use slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = 1,x_2 = 5,y_2 = 6$. Then $m=\frac{6 - 1}{5 - 0}=\frac{5}{5}=1$. But if we take another pair of points, say $(- 5,-4)$ and $(0,1)$. Using the slope formula $m=\frac{1-(-4)}{0 - (-5)}=\frac{1 + 4}{0+5}=\frac{5}{5} = 1$. In terms of the general rise - over - run concept, for every 4 units of run (change in x), there is a 5 units of rise (change in y). The slope $m=\frac{5}{4}$.

Answer:

$\frac{5}{4}$