Q9. - Algebra 1

Question

Use the equation $y=2\left(4+x\right)$ to answer each question.

 

a. Complete the following table for the different values of $x$.

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

$x$	$y$
1
2
3
4
5
6

Step-by-Step Solution

Answer

a. The complete table is given below.

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

b. The plot of these points on coordinate grid is given below.

From the plot, it is observed that these points lie on a straight line.

Part a. Step 1. Define a variable.

A variable in Mathematics is defined as the alphabetic character that expresses a numerical value or a number.

Part a. Step 2. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the sign $"="$.

Part a. Step 3. Complete the table for the given different values of x .

To complete the table place the values of $x$ in $y=2\left(4+x\right)$.

At $x=1$,

$y=2\left(4+1\right)=2\left(5\right)=10$

At $x=2$,

$y=2\left(4+2\right)=2\left(6\right)=12$

At $x=3$,

$y=2\left(4+3\right)=2\left(7\right)=14$

At $x=4$,

$y=2\left(4+4\right)=2\left(8\right)=16$

At $x=5$,

$y=2\left(4+5\right)=2\left(9\right)=18$

At $x=6$,

$y=2\left(4+6\right)=2\left(10\right)=20$

Hence, the complete table is given below.

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

Part b. Step 1. Define a variable.

A variable in Mathematics is defined as the alphabetic character that expresses a numerical value or a number.

Part b. Step 2. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the sign $"="$.

Part b. Step 3. Plot the points from the table on a coordinate grid and notice about the points.

Observe the table.

The points are $\left(1,1\right),\left(2,12\right),\left(3,14\right),\left(4,16\right),\left(5,18\right),\left(6,20\right)$.

The plot of these points on coordinate grid is given below.

From the plot, it is observed that these points lie on a straight line.