Find the equation of the linear function represented by the table below in slope- intercept form.

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Finding the Equation of a Linear Function**

To determine the equation of the linear function represented by the table below in slope-intercept form, follow the instructions and data provided.

**Table: Linear Function Data**

|  x  |  y  |
|:---:|:---:|
| -3  | -5  |
|  2  | 10  |
|  7  | 25  |
| 12  | 40  |

**Explanation:**

The task is to find the equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

**Step 1: Calculate the Slope (m)**

To find the slope (\( m \)), use the formula:

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

Select any two points from the table, for example, (2, 10) and (7, 25).

\[
m = \frac{25 - 10}{7 - 2} = \frac{15}{5} = 3
\]

**Step 2: Find the Y-intercept (b)**

Now use the slope and one of the points to solve for \( b \). Using point (2, 10):

\[
10 = 3(2) + b
\]

\[
10 = 6 + b
\]

\[
b = 4
\]

**Equation of the Line**

Thus, the equation of the linear function is:

\[
y = 3x + 4
\]

Using these steps and calculations, you can determine the linear function represented by the given data.
Transcribed Image Text:**Finding the Equation of a Linear Function** To determine the equation of the linear function represented by the table below in slope-intercept form, follow the instructions and data provided. **Table: Linear Function Data** | x | y | |:---:|:---:| | -3 | -5 | | 2 | 10 | | 7 | 25 | | 12 | 40 | **Explanation:** The task is to find the equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. **Step 1: Calculate the Slope (m)** To find the slope (\( m \)), use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Select any two points from the table, for example, (2, 10) and (7, 25). \[ m = \frac{25 - 10}{7 - 2} = \frac{15}{5} = 3 \] **Step 2: Find the Y-intercept (b)** Now use the slope and one of the points to solve for \( b \). Using point (2, 10): \[ 10 = 3(2) + b \] \[ 10 = 6 + b \] \[ b = 4 \] **Equation of the Line** Thus, the equation of the linear function is: \[ y = 3x + 4 \] Using these steps and calculations, you can determine the linear function represented by the given data.
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