How is slope and constant rate of change the same?

Answer 1

Slope is known as rise over run. Rise means the amount of units the y-value (or second dimension) has traveled up the y-axis or down the y-axis. Run means the amount of units the x-value (the first dimension) has traveled forwards or backwards on the x-axis. Take a slope of 2 (can also be written as 2/1) that means it goes up two units as it goes over 1 unit for the whole entire graph. A slope of 5/7 means it goes with a y-value of 5 up and an x-value of 7 over. This can be done for any number even negative numbers. Ok... so now to relate it to a constant rate of change. Imagine the dimensions (x and y values) go on for an infinite amount. The slope will be constant throughout infinity. It will always have the same rise over run... It will always be constant. The rate of change is equivalent to the saying "rise over run". Since the slope is constant over infinity the constant rate of change is the same thing across infinity.