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

xy

11

33

2

7

3

11

4

15

To find the equation of the linear function in slope-intercept form, we need to determine the slope \( m \) and the y-intercept \( b \) of the line, using the given points in the table:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 1 \\
2 & 3 \\
3 & 7 \\
4 & 11 \\
\hline
\end{array}
\]

### Step 1: Calculate the slope \( m \)
The slope \( m \) of a linear function can be calculated using the formula:

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

Let's take two points from the table, say \( (2, 3) \) and \( (3, 7) \):

\[
m = \frac{7 - 3}{3 - 2} = \frac{4}{1} = 4
\]

So, the slope \( m = 4 \).

### Step 2: Use the slope-intercept form \( y = mx + b \)
Now that we know \( m = 4 \), we substitute it into the slope-intercept form equation:

\[
y = 4x + b
\]

### Step 3: Solve for \( b \) (the y-intercept)
To find \( b \), we use one of the points from the table. Let's use \( (1, 1) \):

\[
1 = 4(1) + b
\]
\[
1 = 4 + b
\]
\[
b = 1 - 4 = -3
\]

### Final Equation
Now that we have both the slope \( m = 4 \) and the y-intercept \( b = -3 \), the equation of the linear function is:

\[
y = 4x - 3
\]

---

Would you like more details on any step or have any questions?

Here are 5 related questions to deepen understanding:

1. What is the general form of a linear equation, and how does it differ from slope-intercept form?
2. Can you find the slope and y-intercept if given two other points from the table?
3. How would the equation change if we only knew one point and the slope?
4. What does the slope of 4 tell us about the behavior of the line?
5. How can you graph this linear function using the equation?

**Tip:** When working with linear equations, always start by identifying the slope first, as it tells you how steep the line is and helps in quickly writing the equation.

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

x y
1 1
2 3
3 7
4 11

Learn how to find the equation of a linear function in slope-intercept form using a given table of values. This problem involves calculating the slope and y-intercept with key algebraic concepts. Suitable for students in Grades 8-10.

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