This week we learned how to calculate the slope of a line. Slope is a number that states how steep a line is. To calculate slope from a graph, you need to find the rise and the run. Those are numbers that describe how to get from one nice point (points on the given line that are not decimals or fractions). The formula for calculating slope is rise over run. It is the same concept if you want to calculate the slope between ordered pairs.
If you take (3,12) and (5,22) as an example, this is how you would calculate the slope.
Calculate the rise and run to get from one nice point to the next. Rise is the rate the line goes up by on the y axis and run is the rate that the line goes horizontally on the x axis. The two ordered pairs (3,12) and (5,22) are both nice points which makes it easier to calculate. Use a slightly modified formula: y1 – y2 over x1 – x2 (the 1 and 2 are refering to the ordered pairs, for example (3,12) is pair one and (5,22) is pair 2). Written out, it should be 12 – 22 over 3 – 5. This should end up becoming -10 over -2. Once you have that you divide -10 by -2 to get an exact answer for the slope. If you graph the two points and the line that passes through them you can verify if the slope is correct. It should look like this:
The slope is 5 over 1 which means to get from one “nice point” to the next closest one you would need to go up 5 units and over 1.