How do we find slope when looking at a graph? What do we use to remember how to find it?
Example Solutions:
m=rise/run, m=the change iny/the change inx, m=y_2-y_1/x_2-x_1
Practice makes perfect
There are several ways to think about the definition of slope. The most basic way to find slope when looking at a graph is to find integer values that the function crosses through and count how many steps up or down and how many steps to the right it took to get from one point to the next. The most mathematical way to define this process is:
m=y_2-y_1/x_2-x_1
where (x_1,y_1) and (x_2,y_2) are two points on the line. This subtraction is often described verbally as:
m=the change iny/the change inx.
This is because the difference between y_2 and y_1 is how much the line changes in the vertical direction and the difference between x_2 and x_1 is how much the line changes in the horizontal direction. The most informal, but arguably most memorable, description of slope is:
m=rise/run,
which describes how we need to divide the amount the line is rising by the amount the line is running.
