Question

Compare Linear function 1 with linear function 2. Which one has the greater rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.

Linear Function 1: y = x + 8

Linear function 2: a graph with (4 , 10) and (2 , 6)

Linear function ___ has the greater rate of change

Answer 1

you sure

Answer 2

To compare the rates of change of the two linear functions, we can determine the slope of each function.

**Linear Function 1:**
The function is given as \( y = x + 8 \). The slope (rate of change) of this function is 1, since it can be expressed in the form \( y = mx + b \) where \( m \) is the slope.

**Linear Function 2:**
For the second function, we can find the slope using the two points \((4, 10)\) and \((2, 6)\). The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in the values from the points:

\[
\text{slope} = \frac{6 - 10}{2 - 4} = \frac{-4}{-2} = 2
\]

Now we can compare the slopes:

- Rate of change (slope) of Linear Function 1: 1
- Rate of change (slope) of Linear Function 2: 2

Since 2 > 1, Linear Function 2 has the greater rate of change.

Therefore:

Linear function **2** has the greater rate of change.

Answer 3

Let’s review the calculations again to ensure accuracy.

**Linear Function 1:**
The function is given as \( y = x + 8 \). The slope (rate of change) is the coefficient of \( x \), which is \( 1 \).

**Linear Function 2:**
We have two points: \((4, 10)\) and \((2, 6)\). To find the slope, we apply the formula:

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the points \((x_1, y_1) = (4, 10)\) and \((x_2, y_2) = (2, 6)\):

\[
\text{slope} = \frac{6 - 10}{2 - 4} = \frac{-4}{-2} = 2
\]

Thus, the rate of change for Linear Function 2 is indeed \( 2 \).

Now comparing the two slopes:

- Linear Function 1 (slope): \( 1 \)
- Linear Function 2 (slope): \( 2 \)

Since \( 2 > 1 \), it confirms that Linear Function 2 has the greater rate of change.

So, my original conclusion stands correct:

**Linear function 2 has the greater rate of change.**