Question

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

Answer 1

Answer:

The function is f(x) =   $\frac{3}{2}$ x + $\frac{9}{2}$  

Step-by-step 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  $\frac{3}{2}$

- The rate of change is the slope of the graph

∴ m =  $\frac{3}{2}$

∵ 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 = $\frac{3}{2}$ (x - 4)

Simplify the right hand side

∴ y - 10.5 =  $\frac{3}{2}$ (x) -  $\frac{3}{2}$ (4)

∴ y - 10.5 =  $\frac{3}{2}$ x - 6

Add 10.5 to both sides

∴ y =  $\frac{3}{2}$ x + 4.5

∵ 4.5 = $\frac{9}{2}$

∴ y =  $\frac{3}{2}$ x + $\frac{9}{2}$

∵ y = f(x)

∴ f(x) =  $\frac{3}{2}$ x + $\frac{9}{2}$

The function is f(x) =   $\frac{3}{2}$ x + $\frac{9}{2}$