Rate of change is defined as the ratio of change in vertical value to change in horizontal value. In other words it is described as the
ratio of change in output to input values. Here the horizontal or input values stand for x and the vertical or output stands for y.
Example 1: A line y = 3x – 4 is passing through the two points (2, 2) and (-5, -19). Find the rate of change of the given points.
Here in (2, 2) input value is 2 and output value is 2
In (-5, -19) input value is -5 and output value is -19
Example 2: Edward has 8 gallons of gasoline in his car. After driving 200 miles he had 4 gallons left. Find the rate of change of
gasoline.
Number of miles he drove is 200
Horizontal change is 200 miles.
Change in amount of gasoline = 4 – 8 = -4
If the travelling distance is increasing then the amount of gasoline decreases. Hence the rate of change shows a negative sign.
Hence Edward’s car is burning 0.02 gallons of gasoline per mile. If the travelling distance is increasing then the amount of gasoline
decreases.
ratio of change in output to input values. Here the horizontal or input values stand for x and the vertical or output stands for y.
Example 1: A line y = 3x – 4 is passing through the two points (2, 2) and (-5, -19). Find the rate of change of the given points.
Here in (2, 2) input value is 2 and output value is 2
In (-5, -19) input value is -5 and output value is -19
Example 2: Edward has 8 gallons of gasoline in his car. After driving 200 miles he had 4 gallons left. Find the rate of change of
gasoline.
Number of miles he drove is 200
Horizontal change is 200 miles.
Change in amount of gasoline = 4 – 8 = -4
If the travelling distance is increasing then the amount of gasoline decreases. Hence the rate of change shows a negative sign.
Hence Edward’s car is burning 0.02 gallons of gasoline per mile. If the travelling distance is increasing then the amount of gasoline
decreases.
