https://file.aiquickdraw.com/mathbot/file/1728327542612x1miwhpk.jpg

The table provided shows values of \(x\) and corresponding values of \(f(x)\). It appears that the table represents a linear function. Let's analyze it to find the equation of the line.

The table gives:
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
3 & 7 \\
4 & 9 \\
5 & 11 \\
6 & 13 \\
\hline
\end{array}
\]

### Step 1: Find the slope (\(m\))
The slope of a line can be calculated using the formula:
\[
m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]
Using the points \( (3, 7) \) and \( (4, 9) \):
\[
m = \frac{9 - 7}{4 - 3} = \frac{2}{1} = 2
\]
So, the slope of the line is \( m = 2 \).

### Step 2: Find the y-intercept (\(b\))
We use the slope-intercept form of the equation of a line: 
\[
f(x) = mx + b
\]
Substituting one of the points, say \( (3, 7) \), into this equation:
\[
7 = 2(3) + b
\]
\[
7 = 6 + b
\]
\[
b = 1
\]

### Final Equation of the Line:
\[
f(x) = 2x + 1
\]

Would you like further details or clarifications on this? Here are 5 additional related questions:

1. How do you calculate the slope if you have two points on a line?
2. What is the significance of the slope in a linear equation?
3. Can you use a different point to calculate the y-intercept and check if the result is the same?
4. How would you graph this linear equation on a coordinate plane?
5. What happens to the slope and y-intercept if you modify the values in the table?

**Tip:** Always ensure the slope is consistent across all pairs of points in a table before concluding that the function is linear.

The table of values represents a linear function, find the equation of the line.

Learn how to find the equation of a line from a table of values with detailed step-by-step solutions. The table provides key points like (3, 7) and (4, 9), and we calculate the slope and y-intercept to derive the linear equation. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation