Question
Writing Simultaneous Linear Equations Quick Check
1 of 51 of 5 Items
Question
Use the table to answer the question.
Table of Values
x ya yb
0 3 18
1 6 13 1/2
2 9 9
Which of the following systems of linear equations does the table of values represent?
(1 point)
Responses
{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
1 of 51 of 5 Items
Question
Use the table to answer the question.
Table of Values
x ya yb
0 3 18
1 6 13 1/2
2 9 9
Which of the following systems of linear equations does the table of values represent?
(1 point)
Responses
{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
Answers
GPT-4o mini
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:
1. {y=3x+3, y=4 1/2x+18}
2. {y=3x+3, y=4 1/2x−18}
3. {y=−3x+3, y=4 1/2x+18}
4. {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.
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:
1. {y=3x+3, y=4 1/2x+18}
2. {y=3x+3, y=4 1/2x−18}
3. {y=−3x+3, y=4 1/2x+18}
4. {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.
Related Questions
Solution Sets of Simultaneous Equations Quick Check
3 of 53 of 5 Items
Question
Use the tab...
Writing Simultaneous Linear Equations Quick Check
1 of 51 of 5 Items
Question
Use the table to...
Solution Sets of Simultaneous Equations Quick Check
3 of 53 of 5 Items
Question
Use the tab...
WRITING SIMULTANEOUS LINEAR EQUATIONS QUICK CHECK:
USE THE TABLE TO ANSWER THE QUESTION.
TABLE OF...