To determine which table represents a linear function with a slope of 5 and a y-intercept of 20, we can use the slope-intercept form of a linear equation, which is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Given that the slope \( m \) is 5 and the y-intercept \( b \) is 20, the equation of the line is:
\[ y = 5x + 20 \]
Now, we can use this equation to calculate the corresponding \( y \) values for a few \( x \) values.
- For \( x = 0 \): \[ y = 5(0) + 20 = 20 \]
- For \( x = 4 \): \[ y = 5(4) + 20 = 20 + 20 = 40 \]
- For \( x = 8 \): \[ y = 5(8) + 20 = 40 + 20 = 60 \]
- For \( x = -4 \): \[ y = 5(-4) + 20 = -20 + 20 = 0 \]
Now, we can summarize the expected values of \( y \) for given \( x \) values:
- If \( x = -4 \), then \( y = 0 \)
- If \( x = 0 \), then \( y = 20 \)
- If \( x = 4 \), then \( y = 40 \)
- If \( x = 8 \), then \( y = 60 \)
Now, let's check the provided tables:
1st Table:
- \( x = -4, y = 0 \)
- \( x = 0, y = 20 \)
- \( x = 4, y = 40 \)
- \( x = 8, y = 60 \)
This table matches our calculated values.
2nd Table:
- \( x = -4, y = 0 \)
- \( x = 0, y = -20 \)
- \( x = 4, y = -40 \)
- \( x = 8, y = -60 \)
This table does not match.
3rd Table:
- \( x = 0, y = -4 \)
- \( x = 20, y = 0 \)
- \( x = 40, y = 4 \)
- \( x = 60, y = 8 \)
This table does not match.
4th Table:
- \( x = -60, y = 8 \)
- \( x = -40, y = 4 \)
- \( x = -20, y = 0 \)
- \( x = 0, y = -4 \)
This table does not match.
Thus, the table that represents a linear function with a slope of 5 and a y-intercept of 20 is the 1st Table.