Question

Use the equation y - 5 = x/3 to fill in the missing values in the table below. When I put BLANK, it means that part of the equation is blank and you need to fill it in.
x: BLANK y: 1
x: -3 y: 4
x: 0 y: BLANK
x: 6 y: BLANK
x: BLANK y: 8

Answer 1

To fill in the missing values in the table using the equation \( y - 5 = \frac{x}{3} \), we'll rearrange the equation to express \( y \) in terms of \( x \):

\[
y = \frac{x}{3} + 5
\]

Now we can calculate the missing values based on the given \( x \) and \( y \) values.

1. **For \( y = 1 \)**:
\[
1 = \frac{x}{3} + 5
\]
Subtract 5 from both sides:
\[
1 - 5 = \frac{x}{3} \implies -4 = \frac{x}{3}
\]
Multiply by 3:
\[
x = -12
\]

So, the first row is \( x: -12, y: 1 \).

2. **For \( x = -3 \)**, find \( y \):
\[
y = \frac{-3}{3} + 5 = -1 + 5 = 4
\]
This confirms the value is correct.

3. **For \( x = 0 \)**, find \( y \):
\[
y = \frac{0}{3} + 5 = 0 + 5 = 5
\]

So, the third row is \( x: 0, y: 5 \).

4. **For \( x = 6 \)**, find \( y \):
\[
y = \frac{6}{3} + 5 = 2 + 5 = 7
\]

So, the fourth row is \( x: 6, y: 7 \).

5. **For \( y = 8 \)**:
\[
8 = \frac{x}{3} + 5
\]
Subtract 5 from both sides:
\[
8 - 5 = \frac{x}{3} \implies 3 = \frac{x}{3}
\]
Multiply by 3:
\[
x = 9
\]

So, the last row is \( x: 9, y: 8 \).

Now, compiling everything, the table looks like this:

- \( x: -12, y: 1 \)
- \( x: -3, y: 4 \)
- \( x: 0, y: 5 \)
- \( x: 6, y: 7 \)
- \( x: 9, y: 8 \)

Here are the missing values:

\[
\text{First Row: } x = -12 \\
\text{Third Row: } y = 5 \\
\text{Fourth Row: } y = 7 \\
\text{Fifth Row: } x = 9
\]