Understand Slope of a Line: example 11.34

Locate two points on the graph, choosing points whose coordinates are integers. We will use $(0,\mathrm{-3})$ and $(5,1).$

Starting with the point on the left, $(0,\mathrm{-3}),$ sketch a right triangle, going from the first point to the second point, $(5,1).$

Count the rise on the vertical leg of the triangle.	The rise is 4 units.
Count the run on the horizontal leg.	The run is 5 units.
Use the slope formula.	$m=\frac{\text{rise}}{\text{run}}$
Substitute the values of the rise and run.	$m=\frac{4}{5}$
	The slope of the line is $\frac{4}{5}$.

Notice that the slope is positive since the line slants upward from left to right.