To determine which systems of linear equations the table of values represents, we will analyze the two sets of values (ya and yb) given in the table.
From the table:
For ya:
- When \( x = 0 \), \( ya = 3 \)
- When \( x = 1 \), \( ya = 6 \)
- When \( x = 2 \), \( ya = 9 \)
The values of \( ya \) increase by 3 as \( x \) increases by 1. This means the slope (m) is 3. Using the point (0, 3) to find the y-intercept (b), we get:
- The equation for ya can be written as \( y = 3x + 3 \).
For yb:
- When \( x = 0 \), \( yb = 18 \)
- When \( x = 1 \), \( yb = 13.5 \)
- When \( x = 2 \), \( yb = 9 \)
The values of \( yb \) decrease by 4.5 as \( x \) increases by 1. The slope (m) is -4.5. We can find the y-intercept using the point (0, 18):
- The equation for yb can be written as \( y = -4.5x + 18 \).
Now, looking at the response options:
- {y=3x+3, y=4 1/2x+18}
- {y=3x+3, y=4 1/2x−18}
- {y=−3x+3, y=4 1/2x+18}
- {y=3x+3, y=4 1/2x+18}
The correct equations that match with our calculations are:
- \( ya: y = 3x + 3 \)
- \( yb: y = -4.5x + 18 \)
However, none of the options accurately identifies \( yb \) since the slope should be negative. The closest representation appears to be a misunderstanding in the slope formatting.
Upon reviewing the current options carefully, the only valid choice for ya is {y=3x+3}, but we do not find an exact match for yb. If formatting has created confusion, it seems yb has not been correctly assessed in what's given.
Therefore consider the option: {y=3x+3, y=4 1/2x+18}, given the lack of alternatives, it may indicate a misrepresentation of slope interpretation but fits the equation structures formed.
In conclusion: The best choice would be: {y=3x+3, y=4 1/2x+18} however, the correct interpretation of \( yb \) has discrepancies so it's essential to verify context. Please confirm any further defining information on slope values for proper selection.
1 answer