Question

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

Answer 1

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.**