Q11. - Algebra 1

Question

Use the equation $\mathbf{y}\mathbf{=}\mathbf{2}\mathbf{(}\mathbf{4}\mathbf{+}\mathbf{x}\mathbf{)}$ to answer each question.

a. Complete the table for each value of x.

b. Plot the points from the table on a coordinate grid. What do you notice about the points?

c. Make a conjecture about the relationship between the change in x and the change in y.

Step-by-Step Solution

Answer

a. The complete table is as follows:

x	y
1	10
2	12
3	14
4	16
5	18
6	20

b. The graph is shown in Figure (1) and the points on the graph represents a straight line.

c. The conjecture about the relationship between the change in x and change in y is as follows:
When x increases by 1 unit, then y increases by 2 units.

Part a. Step 1. Given Information.

Given that,

The equation is $y=2(4+x)$ 

Part a. Step 2. Calculation.

Put $x=1$ in the given equation, we get

$$\begin{gathered} y=2\left(4+1\right) \\ =2\left(5\right) \\ =10 \end{gathered}$$

 

Put $x=2$ in the given equation, we get

$$\begin{gathered} y=2\left(4+2\right) \\ =2\left(6\right) \\ =12 \end{gathered}$$

Put $x=3$ in the given equation, we get

$$\begin{gathered} y=2\left(4+3\right) \\ =2\left(7\right) \\ =14 \end{gathered}$$

Put $x=4$ in the given equation, we get

$$\begin{gathered} y=2\left(4+4\right) \\ =2\left(8\right) \\ =16 \end{gathered}$$

Put $x=5$ in the given equation, we get

$$\begin{gathered} y=2\left(4+5\right) \\ =2\left(9\right) \\ =18 \end{gathered}$$

Put $x=6$ in the given equation, we get

$$\begin{gathered} y=2\left(4+6\right) \\ =2\left(10\right) \\ =20 \end{gathered}$$

Part a. Step 3. Complete the table for each value of x.

The table becomes:

 

x	y
1	10
2	12
3	14
4	16
5	18
6	20

 

Part b. Step 1. Given Information.

The table from part (a) is as follows:

x	y
1	10
2	12
3	14
4	16
5	18
6	20

Part b. Step 2. Plot the points from the table on coordinate grid.

By using the table, the graph becomes

Figure (1)

Part b. Step 3. Interpretation about the points.

From the graph, we can see that,

The points represent a straight line.

Therefore,

The graph is shown in Figure (1) and the points on the graph represents a straight line.

Part c. Step 1. Given Information.

The table from part (a) is as follows:

x	y
1	10
2	12
3	14
4	16
5	18
6	20

Part c. Step 2. Concept used.

In the table, we have to see that how x changes and how y changes.

And

Then we have to find the relationship between how x changes and how y changes.

Part c. Step 3. Make a conjecture about the relationship between the change in x and the change in y.

In the table, we can see that,

When x changes by 1 unit, then y is changing by 2 units.

Therefore,

The conjecture about the relationship between the change in x and change in y is as follows:

When x increases by 1 unit, then y increases by 2 units.