Which table contains only values that satisfy the equation *y* = 7*x* + 0.5?

A.

***x***

***y***

0

0

2

14.5

4

28.5

6

42.5

B.

***x***

***y***

0

0.5

2

14.5

4

28.5

6

42.5

C.

***x***

***y***

0

0.5

2

9.5

4

11.5

6

13.5

D.

***x***

***y***

0

0.5

2

15.5

4

29.5

6

43.5


The given equation is:

\[
y = 7x + 0.5
\]

We will evaluate each table to see which one has values that satisfy this equation.

### Checking Table A:
1. For \(x = 0\): \(y = 7(0) + 0.5 = 0.5\), but the table shows \(y = 0\). Not a match.
2. So, Table A does not satisfy the equation.

### Checking Table B:
1. For \(x = 0\): \(y = 7(0) + 0.5 = 0.5\), which matches.
2. For \(x = 2\): \(y = 7(2) + 0.5 = 14 + 0.5 = 14.5\), which matches.
3. For \(x = 4\): \(y = 7(4) + 0.5 = 28 + 0.5 = 28.5\), which matches.
4. For \(x = 6\): \(y = 7(6) + 0.5 = 42 + 0.5 = 42.5\), which matches.

All values in Table B satisfy the equation.

### Checking Table C:
1. For \(x = 0\): \(y = 7(0) + 0.5 = 0.5\), which matches.
2. For \(x = 2\): \(y = 7(2) + 0.5 = 14 + 0.5 = 14.5\), but the table shows \(y = 9.5\). Not a match.
3. So, Table C does not satisfy the equation.

### Checking Table D:
1. For \(x = 0\): \(y = 7(0) + 0.5 = 0.5\), which matches.
2. For \(x = 2\): \(y = 7(2) + 0.5 = 14 + 0.5 = 14.5\), but the table shows \(y = 15.5\). Not a match.
3. So, Table D does not satisfy the equation.

### Conclusion:
The correct answer is **Table B**, as it is the only one that contains values satisfying the equation \(y = 7x + 0.5\).

Would you like more details on this solution, or do you have any other questions?

Here are five related questions to explore further:
1. How do you determine if a set of points lies on a given linear equation?
2. What is the slope-intercept form of a linear equation?
3. How would you graph the equation \(y = 7x + 0.5\)?
4. What does the slope represent in the equation \(y = 7x + 0.5\)?
5. How do you find the y-intercept of a linear equation?

**Tip:** When verifying points for a linear equation, always substitute the values of \(x\) and check if the calculated \(y\) matches the one in the table.

Which table contains only values that satisfy the equation y = 7x + 0.5?

Explore which table contains values that satisfy the linear equation y = 7x + 0.5. Learn how to verify values and apply the slope-intercept form of a line. This problem covers key algebra concepts for Grades 6-8.

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