Assuming a linear relationship, find the missing value in the table below.
y
x
1
2
3
4
5
1
3
5
7

To find the missing value, we can first identify the relationship between \(x\) and \(y\) by observing the given points.

The table is as follows:

| \(x\) | \(y\) |
|------|------|
| 1    | ?    |
| 2    | 1    |
| 3    | 3    |
| 4    | 5    |
| 5    | 7    |

From the values of \(y\) at \(x = 2\), \(x = 3\), \(x = 4\), and \(x = 5\), we can observe that for each increase of 1 in \(x\), the corresponding increase in \(y\) is 2.

This suggests a linear relationship with a slope of 2. To confirm this, let's write the equation of the line in the form:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

Since the slope \(m = 2\), we now substitute any point from the table to solve for \(b\). Using the point \( (x = 2, y = 1) \):

\[
1 = 2(2) + b \implies 1 = 4 + b \implies b = -3
\]

Thus, the equation of the line is:

\[
y = 2x - 3
\]

Now, we substitute \(x = 1\) into the equation to find the missing \(y\)-value:

\[
y = 2(1) - 3 = 2 - 3 = -1
\]

So, the missing \(y\)-value when \(x = 1\) is \(-1\).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the general form of a linear equation?
2. How do you calculate the slope between two points?
3. Can linear relationships have different types of slopes (positive, negative, zero)?
4. How would the equation change if the slope were negative?
5. How can we interpret the slope in real-world contexts?

**Tip:** Always check the pattern in a table by calculating the difference between values to identify possible relationships.

Assuming a linear relationship, find the missing value in the table below.

Discover how to find the missing value in a linear table by applying the equation y = 2x - 3. This problem focuses on linear relationships, slope-intercept form, and solving for unknowns. Perfect for Grades 6-8 students.

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