Question

Consider the following two points:

A (4,3)
B (8,4)
What is the rate of shange of the line AB?
Answer as a decimal.

Answer 1

The rate of change of line AB is 0.25

Explanation:

• The average rate of change is constant for a linear function.
• The average rate of change of linear function y = m x + b is the value of m over any interval
• The formula of m is
  `m=(y_(2)-y_(1))/(x_(2)-x_(1))`

∵ The coordinates of point A are (4 , 3)

∵ The coordinates of point B are (8 , 4)

∴
`x_(1)` = 4 and
`x_(2)` = 8

∴
`y_(1)` = 3 and
`y_(2)` = 4

- Substitute their value in the formula of the slope above

∵
`m=(4-3)/(8-4)=(1)/(4)`

∵
`(1)/(4)` = 0.25

∴ m = 4

- The rate of change of a line is the slope of the line

∴ The rate of change of line AB is 0.25