Question

The function with a rate of change of 3/2 whose graph passes through the point (4,10.5)

Answer 1

The function is f(x) =
`(3)/(2)` x +
`(9)/(2)`

Explanation:

The point-slope form of a linear function is
`y-y_(1)=m(x - x_(1))` , where

• m is the slope of the graph (rate of change)
• (
  `x_(1)` ,
  `y_(1)`) is a point on the line (the line passes through it)

∵ The function has a rate of change
`(3)/(2)`

- The rate of change is the slope of the graph

∴ m =
`(3)/(2)`

∵ The graph is passes through point (4 , 10.5)

∴
`x_(1)` = 4 and
`y_(1)` = 10.5

Substitute m and the coordinates of the point in the form of the equation

∵
`y-y_(1)=m(x - x_(1))`

∴ y - 10.5 =
`(3)/(2)` (x - 4)

Simplify the right hand side

∴ y - 10.5 =
`(3)/(2)` (x) -
`(3)/(2)` (4)

∴ y - 10.5 =
`(3)/(2)` x - 6

Add 10.5 to both sides

∴ y =
`(3)/(2)` x + 4.5

∵ 4.5 =
`(9)/(2)`

∴ y =
`(3)/(2)` x +
`(9)/(2)`

∵ y = f(x)

∴ f(x) =
`(3)/(2)` x +
`(9)/(2)`

The function is f(x) =
`(3)/(2)` x +
`(9)/(2)`