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Alex17521 [72]
3 years ago
13

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

Mathematics
1 answer:
irina1246 [14]3 years ago
5 0

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}  

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