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

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!