Question
linear function contains the three ordered pairs shown in the table.
Create an equation for a different linear function that has twice the rate of change and the same initial value as the one represented by the table.linear function contains the three ordered pairs shown in the table.
Create an equation for a different linear function that has twice the rate of change and the same initial value as the one represented by the table.
Create an equation for a different linear function that has twice the rate of change and the same initial value as the one represented by the table.linear function contains the three ordered pairs shown in the table.
Create an equation for a different linear function that has twice the rate of change and the same initial value as the one represented by the table.
Answers
Answered by
GPT-4o mini
To create an equation for a different linear function that has twice the rate of change and the same initial value as another linear function represented by a table, you'll need to follow these steps:
1. **Identify the current linear function**: The general form of a linear function is \( y = mx + b \), where \( m \) is the rate of change (slope) and \( b \) is the initial value (y-intercept).
2. **Determine the slope and y-intercept**: From the table (which you haven't provided), you'd typically identify the slope from the pairs given. The slope can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1)\) and \((x_2, y_2)\) are two points from the ordered pairs. The y-intercept \( b \) would typically be one of the \( y \) values where \( x = 0 \), or it can be derived using one of the points and the slope.
3. **Create the new linear function**:
- The new rate of change will be \( 2m \) (twice the original).
- The initial value remains the same, which is \( b \).
- Therefore, your new linear function will be:
\[
y = 2m \cdot x + b
\]
### Example
Let's say the original rate of change (slope) based on your table is \( m = 3 \) and the initial value (y-intercept) is \( b = 5 \). Then the new linear function that has twice the rate of change would be:
1. Calculate the new slope:
\[
2m = 2 \cdot 3 = 6
\]
2. Keep the same initial value:
\[
b = 5
\]
3. Write the new equation:
\[
y = 6x + 5
\]
### Final Note
Since you haven’t provided the specific values from the table, you need to replace \( m \) and \( b \) with the actual values identified from your table to get the specific equation. If you provide the ordered pairs, I can give you a more precise example!
1. **Identify the current linear function**: The general form of a linear function is \( y = mx + b \), where \( m \) is the rate of change (slope) and \( b \) is the initial value (y-intercept).
2. **Determine the slope and y-intercept**: From the table (which you haven't provided), you'd typically identify the slope from the pairs given. The slope can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1)\) and \((x_2, y_2)\) are two points from the ordered pairs. The y-intercept \( b \) would typically be one of the \( y \) values where \( x = 0 \), or it can be derived using one of the points and the slope.
3. **Create the new linear function**:
- The new rate of change will be \( 2m \) (twice the original).
- The initial value remains the same, which is \( b \).
- Therefore, your new linear function will be:
\[
y = 2m \cdot x + b
\]
### Example
Let's say the original rate of change (slope) based on your table is \( m = 3 \) and the initial value (y-intercept) is \( b = 5 \). Then the new linear function that has twice the rate of change would be:
1. Calculate the new slope:
\[
2m = 2 \cdot 3 = 6
\]
2. Keep the same initial value:
\[
b = 5
\]
3. Write the new equation:
\[
y = 6x + 5
\]
### Final Note
Since you haven’t provided the specific values from the table, you need to replace \( m \) and \( b \) with the actual values identified from your table to get the specific equation. If you provide the ordered pairs, I can give you a more precise example!