To find the slope and y-intercept of the linear function represented by the table, we'll first need to look for the change in \( y \) over the change in \( x \) (which gives you the slope), and then find the value of \( y \) when \( x = 0 \) (which gives you the y-intercept).
From the data you provided, it seems like the table of values for \( x \) and \( y \) is as follows:
- When \( x = -3 \), \( y = 1 \)
- When \( x = 0 \), \( y = 12 \)
- When \( x = 3 \), \( y = 36 \)
- When \( x = 6 \), \( y = 60 \)
Step 1: Calculate the Slope (m)
The slope can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We can choose two points from the data, for example, \( (0, 12) \) and \( (3, 36) \): \[ m = \frac{36 - 12}{3 - 0} = \frac{24}{3} = 8 \]
So, the slope \( m \) is 8.
Step 2: Calculate the y-intercept (b)
The y-intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 12 \).
So, the y-intercept \( b \) is 12.
Final Answers
- The slope is 8.
- The y-intercept is 12.
Summary:
- The slope is 8.
- The y-intercept is 12.