Question

Assuming a linear relationship, find the missing value in the table below.
y
x
1
2
3
4
5
12
14
16
18

Answer 1

To find the missing value in the table and assume a linear relationship between \( x \) and \( y \), we first need to establish a linear equation of the form:

\[
y = mx + b
\]

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

From the provided data:

For the values of \( x \):
- \( x = 1 \), \( y = 12 \)
- \( x = 2 \), \( y = 14 \)
- \( x = 3 \), \( y = 16 \)
- \( x = 4 \), \( y = 18 \)
- \( x = 5 \), \( y = ? \)

Let's calculate the slope \( m \) using the first two points:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{14 - 12}{2 - 1} = \frac{2}{1} = 2
\]

Now we can use the slope to find the linear equation. We can use one of the known points to solve for \( b \).

Using the point \( (1, 12) \):

\[
y = mx + b \implies 12 = 2(1) + b \implies 12 = 2 + b \implies b = 12 - 2 = 10
\]

The equation of the line is:

\[
y = 2x + 10
\]

Now we can substitute \( x = 5 \) to find the missing value of \( y \):

\[
y = 2(5) + 10 = 10 + 10 = 20
\]

Thus, the missing value when \( x = 5 \) is:

\[
\boxed{20}
\]