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The table provides data points for a linear function, and we are tasked with finding the equation in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Find the slope (\( m \))
The slope is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can use any two points from the table. Let's take the points \( (1, 0) \) and \( (2, 5) \):
\[
m = \frac{5 - 0}{2 - 1} = \frac{5}{1} = 5
\]

### Step 2: Find the y-intercept (\( b \))
To find \( b \), we can use the slope-intercept form and one of the points. Using \( (1, 0) \) (since it's easy to work with):
\[
y = mx + b
\]
Substitute \( x = 1 \), \( y = 0 \), and \( m = 5 \):
\[
0 = 5(1) + b
\]
\[
b = 0 - 5 = -5
\]

### Step 3: Final equation
Thus, the equation of the linear function is:
\[
y = 5x - 5
\]

Would you like more details on the solution, or do you have any questions?

### Related Questions:
1. How would the equation change if one of the points were different?
2. Can you explain how the slope is consistent across all the points?
3. What if we were asked to find the equation in standard form instead of slope-intercept form?
4. How can you tell that the given table represents a linear function?
5. How would you calculate the slope if the table had different increments for \( x \)?

### Tip:
When solving for the slope, using points that are easy to work with (like integers) simplifies the calculation process.

Find the equation of the linear function represented by the table below in slope-intercept form. The table contains the following data points: (1, 0), (2, 5), (3, 10), (4, 15).

Find the equation of a linear function using table data points (1, 0), (2, 5), (3, 10), and (4, 15). Learn to calculate the slope and the y-intercept step-by-step, and write the equation in slope-intercept form: y = mx + b.

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