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Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?

Linear Function 1: y=15x+8
y
=
15
x
+
8

Linear Function 2:
x
x
y
y

5 26
13 34

1 answer

To compare the rates of change of the two linear functions, we first examine the slope of each function.

Linear Function 1 is given by the equation: \[ y = 15x + 8 \] Here, the coefficient of \(x\) (which is 15) represents the rate of change or the slope of the function. So, the rate of change for Linear Function 1 is: \[ \text{Rate of change (Linear Function 1)} = 15 \]

Linear Function 2 is provided through points:

  • \( (5, 26) \)
  • \( (13, 34) \)

To determine the rate of change (slope) of Linear Function 2, we can use the slope formula, which is given by: \[ \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points:

  • Point 1: \( (x_1, y_1) = (5, 26) \)
  • Point 2: \( (x_2, y_2) = (13, 34) \)

Substituting the values into the slope formula: \[ \text{Slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]

So, the rate of change for Linear Function 2 is: \[ \text{Rate of change (Linear Function 2)} = 1 \]

Conclusion:

Now we can compare the rates of change:

  • Rate of change of Linear Function 1 = 15
  • Rate of change of Linear Function 2 = 1

Linear Function 1 has the greater rate of change.