https://file.aiquickdraw.com/mathbot/file/1728156783784f9w83b3v.jpg

Let's analyze the table and find the equation of the linear function in slope-intercept form.

The table given is:

\[
\begin{array}{c|c}
x & y \\
\hline
1 & 1 \\
2 & 4 \\
3 & 7 \\
4 & 10 \\
\end{array}
\]

We need to find the equation in the form \( y = mx + b \), where:
- \( m \) is the slope.
- \( b \) is the y-intercept.

### Step 1: Calculate the slope (\( m \))
The slope formula for two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Using the first two points (1, 1) and (2, 4):

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

So, the slope \( m = 3 \).

### Step 2: Find the y-intercept (\( b \))
Now that we know the slope, we can use one of the points (say \( (1, 1) \)) to find the y-intercept. Plugging into the equation \( y = mx + b \):

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

\[
1 = 3 + b \quad \Rightarrow \quad b = 1 - 3 = -2
\]

### Step 3: Write the equation
The equation of the linear function is:

\[
y = 3x - 2
\]

If you have any questions or need more details, feel free to ask!

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Here are 5 related questions you might find helpful:
1. How do you calculate the slope between two points in general?
2. What is the significance of the y-intercept in a linear equation?
3. How can we determine if a function is linear from a table of values?
4. What happens to the slope if the points are reversed in the slope formula?
5. Can you graph this linear function to verify the solution?

**Tip:** Always check that the slope is consistent between multiple points in the table to confirm linearity.

Find the equation of the linear function represented by the table below in slope-intercept form. Table: x = [1, 2, 3, 4], y = [1, 4, 7, 10].

Learn how to find the equation of a linear function using the points from a table. This problem involves calculating the slope and the y-intercept, providing a step-by-step guide to solving the equation in slope-intercept form. Suitable for students in Grades 6-8.

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