To find the equation in slope-intercept form \( y = mx + b \) from the given data points, we first need to calculate the slope \( m \) and the y-intercept \( b \).
Step 1: Identify the points from the table
Based on your table, the points are:
- (0, 4)
- (6, 6)
- (12, 8)
- (18, 10)
Step 2: Calculate the slope \( m \)
The formula for the slope \( m \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We can use any two points. Let's take the points (0, 4) and (6, 6):
\[ m = \frac{6 - 4}{6 - 0} = \frac{2}{6} = \frac{1}{3} \]
Step 3: Calculate the y-intercept \( b \)
Using the slope \( m = \frac{1}{3} \) and one of the points (0, 4), we can find \( b \):
Since \( x = 0 \), we substitute into the equation:
\[ y = mx + b \Rightarrow 4 = \left(\frac{1}{3}\right)(0) + b \Rightarrow b = 4 \]
Step 4: Write the equation
Now we have the values for \( m \) and \( b \):
\[ y = \frac{1}{3}x + 4 \]
Final Equation
Thus, the equation in slope-intercept form based on the data provided is:
\[ y = \frac{1}{3}x + 4 \]
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