To write a linear equation in the form \( y = mx + b \), we need to identify the slope \( m \) and the y-intercept \( b \) from the provided data points.
Given the points from the table:
- (2, 8)
- (4, 15)
- (6, 22)
Step 1: Calculate the slope \( m \)
The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the first two points (2, 8) and (4, 15): \[ m = \frac{15 - 8}{4 - 2} = \frac{7}{2} = 3.5 \]
Step 2: Find the y-intercept \( b \)
We can use one of the points and the slope to find the y-intercept \( b \). We can use the point (2, 8): \[ y = mx + b \] Substituting the values: \[ 8 = 3.5(2) + b \] \[ 8 = 7 + b \] \[ b = 8 - 7 = 1 \]
Step 3: Write the equation
Now, substituting \( m \) and \( b \) back into the linear equation format: \[ y = 3.5x + 1 \]
Therefore, the equation that represents the relationship between \( x \) and \( y \) in the given table is: \[ y = 3.5x + 1 \]