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The table provided asks for the linear equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Let's analyze the table to extract the dataThe table provided asks for the linear equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Let's analyze the table to extract the 

| \( x \) | \( y \)  |
|-------|-------|
| 3     | 47    |
| 4     | 48    |
| 5     | 49    |
| 6     | 50    |

### Step 1: Find the slope (\( m \))
The slope (\( m \)) is calculated using the formula:
\[
m = \frac{{y_2 - y_1}}{{x_2 - x_1}}
\]
We can take any two points from the table to find the slope. Using the points \( (3, 47) \) and \( (4, 48) \):

\[
m = \frac{{48 - 47}}{{4 - 3}} = \frac{1}{1} = 1
\]

### Step 2: Find the y-intercept (\( b \))
To find \( b \), we use the equation \( y = mx + b \) with one of the points, say \( (3, 47) \):
\[
47 = 1(3) + b
\]
\[
47 = 3 + b
\]
\[
b = 47 - 3 = 44
\]

### Final Equation:
The linear equation is:
\[
y = x + 44
\]

Would you like further explanation or have any questions?

Here are 5 related questions:
1. What is the general form of a linear equation?
2. How do you calculate the slope from two points on a line?
3. What does the slope represent in a linear equation?
4. How can we find the y-intercept if the slope is known?
5. How do you determine if a function is linear by looking at a table?

**Tip**: For a linear function, the slope between any two points will always be the same!

Write the linear equation that gives the rule for this table:
 x: 3, 4, 5, 6 
 y: 47, 48, 49, 50

Learn how to find the linear equation from a table of values (x: 3, 4, 5, 6 and y: 47, 48, 49, 50). This problem demonstrates the key algebraic concepts of slope calculation and finding the y-intercept, using the formula y = mx + b.

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