Answer:
The function is f(x) = [tex]\frac{3}{2}[/tex] x + [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
The point-slope form of a linear function is [tex]y-y_{1}=m(x - x_{1})[/tex] , where
∵ The function has a rate of change [tex]\frac{3}{2}[/tex]
- The rate of change is the slope of the graph
∴ m = [tex]\frac{3}{2}[/tex]
∵ The graph is passes through point (4 , 10.5)
∴ [tex]x_{1}[/tex] = 4 and [tex]y_{1}[/tex] = 10.5
Substitute m and the coordinates of the point in the form of the equation
∵ [tex]y-y_{1}=m(x - x_{1})[/tex]
∴ y - 10.5 = [tex]\frac{3}{2}[/tex] (x - 4)
Simplify the right hand side
∴ y - 10.5 = [tex]\frac{3}{2}[/tex] (x) - [tex]\frac{3}{2}[/tex] (4)
∴ y - 10.5 = [tex]\frac{3}{2}[/tex] x - 6
Add 10.5 to both sides
∴ y = [tex]\frac{3}{2}[/tex] x + 4.5
∵ 4.5 = [tex]\frac{9}{2}[/tex]
∴ y = [tex]\frac{3}{2}[/tex] x + [tex]\frac{9}{2}[/tex]
∵ y = f(x)
∴ f(x) = [tex]\frac{3}{2}[/tex] x + [tex]\frac{9}{2}[/tex]
The function is f(x) = [tex]\frac{3}{2}[/tex] x + [tex]\frac{9}{2}[/tex]
