Table of Values - Examples, Exercises and Solutions

A value table is the "preparatory work" that we are often asked to do before producing a graphical representation. Therefore, it is an inseparable part of the subject of graphs in general and the topic of functions in particular.

What is a Value Table?

A value table is actually a database, on which a discrete or continuous graph is based.
The data table lists the corresponding value of Y Y for each X X .
The value table allows you to project and draw the graph conveniently and efficiently.
Below is an example of a value table for the function Y=X+2 Y=X+2

Image -- an example of a value table for the function Y = X + 21

Based on this value table, the following linear function can be plotted:

Practice Table of Values

Examples with solutions for Table of Values

Exercise #1

Calculate y given that x=2 x=2 and y=x y=x .

Video Solution

Step-by-Step Solution

We are given the equation y=x

We are also given the value of x, 

x=2

Therefore, we will insert the given value into the equation

y=2

And that's the solution!

Answer

2 2

Exercise #2

Find a y when x=2 x=2

y=5x y=5x

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given equation y=5x y = 5x .
  • Step 2: Substitute the value x=2 x = 2 into the equation.
  • Step 3: Calculate the value of y y .

Now, let's work through each step:
Step 1: We start with the equation y=5x y = 5x .
Step 2: Substitute x=2 x = 2 into this equation:
y=5×2 y = 5 \times 2 .
Step 3: Perform the multiplication:
y=10 y = 10 .

Therefore, the solution to the problem is y=10 y = 10 .

Answer

10

Exercise #3

Find a y when x=2

y=12x y=\frac{1}{2}x

Video Solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Substitute the given value of x x into the equation.
  • Step 2: Perform the calculations to find y y .

Now, let's work through each step:
Step 1: The equation provided is y=12x y = \frac{1}{2}x . We need to find the value of y y when x=2 x = 2 .
Step 2: Substitute x=2 x = 2 into the equation:

y=12×2 y = \frac{1}{2} \times 2

Simplifying this expression gives:

y=22 y = \frac{2}{2}

Therefore,

y=1 y = 1 .

The calculated value of y y is 1 1 .

Answer

1 1

Exercise #4

Find a y when x=2

y=x8 y=x-8

Video Solution

Step-by-Step Solution

To solve the problem, we will follow these steps:

  • Step 1: Substitute the given value of x x into the equation y=x8 y = x - 8 .

  • Step 2: Simplify the expression to find the corresponding value of y y .

Now, let's apply these steps:

Step 1: Given the equation y=x8 y = x - 8 , we substitute x=2 x = 2 :
yamp;=28 \begin{aligned} y &= 2 - 8 \end{aligned}

Step 2: Simplify the expression:
yamp;=6 \begin{aligned} y &= -6 \end{aligned}

Thus, the value of y y when x=2 x = 2 is 6-6.

Therefore, the solution to the problem is y=6 y = -6 .

Answer

6 -6

Exercise #5

Calculate y given that X=2 X=2 and y=0.8x y=0.8x .

Video Solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Identify the given information

  • Step 2: Apply the formula

  • Step 3: Perform the calculation

Now, let's work through each step:
Step 1: The problem gives us that x=2 x = 2 and the relationship between y y and x x is y=0.8x y = 0.8x .
Step 2: We will use the formula y=0.8×x y = 0.8 \times x .
Step 3: Substituting x=2 x = 2 into the formula, we get y=0.8×2 y = 0.8 \times 2 .

The calculation is as follows:
y=0.8×2=1.6 y = 0.8 \times 2 = 1.6 .

Therefore, the solution to the problem is y=1.6 y = 1.6 .

Answer

1.6

Exercise #6

Find a y y when x=2

y=30x6 y=30x-6

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Substitute the given value of x x into the equation y=30x6 y = 30x - 6 .

  • Perform the necessary arithmetic to solve for y y .

Now, let's work through these steps:
Step 1: The problem gives us x=2 x = 2 and the equation y=30x6 y = 30x - 6 .
Step 2: Substitute x=2 x = 2 into the equation:
y=30(2)6 y = 30(2) - 6

Step 3: Calculate the expression:
yamp;=30×26yamp;=606yamp;=54 \begin{aligned} y &= 30 \times 2 - 6 \\ y &= 60 - 6 \\ y &= 54 \end{aligned}

The solution to the problem is y=54 y = 54 .

Answer

54

Exercise #7

Find a y when x=2

y=8x+1 y=8x+1

Video Solution

Step-by-Step Solution

To solve this problem, we’ll follow these steps:

  • Step 1: Substitute the given value of x x into the equation.
  • Step 2: Perform the arithmetic calculation to find y y .

Let’s work through each step:

Step 1: Our given equation is y=8x+1 y = 8x + 1 . We substitute x=2 x = 2 into the equation:

y=8(2)+1 y = 8(2) + 1

Step 2: Calculate the expression:

y=16+1 y = 16 + 1

y=17 y = 17

Therefore, when x=2 x = 2 , the value of y y is 17 17 .

Answer

17

Exercise #8

Calculate y given that x=2 x=2 and y=4(26x) y=4(2-6x) .

Video Solution

Step-by-Step Solution

To solve for y y , we will proceed with these steps:

  • Step 1: Substitute the given value x=2 x = 2 into the equation y=4(26x) y = 4(2 - 6x) .
  • Step 2: Simplify the expression inside the parentheses.
  • Step 3: Perform the arithmetic operations to find y y .

Now, let's work through the steps:

Step 1: Substitute x=2 x = 2 into the equation:
y=4(26×2) y = 4(2 - 6 \times 2)

Step 2: Simplify the expression within the parentheses:
26×2=212=10 2 - 6 \times 2 = 2 - 12 = -10

Step 3: Calculate the value of y y by multiplying by 4:
y=4×(10)=40 y = 4 \times (-10) = -40

Therefore, the value of y y is 40-40.

This solution corresponds to the choice:

Choice 3: 40-40

Answer

40 -40

Exercise #9

Find a y when x=2

y=18(x2) y=18(x-2)

Video Solution

Step-by-Step Solution

To solve this problem, we need to substitute x=2 x = 2 into the given expression for y y .

  • Step 1: Write down the expression for y y : y=18(x2) y = 18(x - 2) .
  • Step 2: Substitute x=2 x = 2 into the expression.
  • Step 3: Simplify the expression.

Let's perform these steps:

Step 1: The expression given is y=18(x2) y = 18(x - 2) .

Step 2: Substitute x=2 x = 2 into the expression:
y=18(22) y = 18(2 - 2) .

Step 3: Simplify the expression:
Since 22=0 2 - 2 = 0 , we have y=18×0=0 y = 18 \times 0 = 0 .

Therefore, when x=2 x = 2 , the value of y y is 0 0 .

Answer

0 0

Exercise #10

Find y y when x=2 x=2

y=25x+2 y=\frac{2}{5}x+2

Video Solution

Step-by-Step Solution

In this exercise, we are given the value of X, so we will substitute it into the formula.

It's important to remember that between an unknown and a number there is a multiplication sign, therefore:

y=25(2)+2 y=\frac{2}{5}\cdot(2)+2

y=45+2 y=\frac{4}{5}+2

Let's convert to a decimal fraction:

y=0.8+2 y=0.8+2
y=2.8 y=2.8

And that's the solution!

Answer

2.8 2.8

Exercise #11

Find a y when x=2

y=5.6x2.1 y=5.6x-2.1

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Identify the given equation and variable.
  • Step 2: Substitute the given value of x x into the equation.
  • Step 3: Perform the necessary arithmetic to calculate y y .

Now, let's work through each step:
Step 1: The equation given is y=5.6x2.1 y = 5.6x - 2.1 . We need to find y y when x=2 x = 2 .
Step 2: Substitute x=2 x = 2 into the equation:
y=5.6(2)2.1 y = 5.6(2) - 2.1 .
Step 3: Calculate y y by performing the arithmetic:
First, calculate the multiplication: 5.6×2=11.2 5.6 \times 2 = 11.2 .
Then, subtract 2.1 from 11.2: 11.22.1=9.1 11.2 - 2.1 = 9.1 .

Therefore, the solution to the problem is y=9.1 y = 9.1 .

Answer

9.1

Exercise #12

Find a y when x=2

y=2+6x y=2+6x

Video Solution

Step-by-Step Solution

To solve this problem, we'll substitute the given value of x=2 x = 2 into the equation y=2+6x y = 2 + 6x .
1. Substitute x=2 x = 2 into the equation:
yamp;=2+6xamp;=2+6×2 \begin{aligned} y &= 2 + 6x \\ &= 2 + 6 \times 2 \end{aligned}

2. Perform the multiplication 6×2 6 \times 2 :
6×2=12 6 \times 2 = 12

3. Add the result to 2:
yamp;=2+12amp;=14 \begin{aligned} y &= 2 + 12 \\ &= 14 \end{aligned}

Thus, when x=2 x = 2 , the value of y y is 14\mathbf{14}.

Answer

14

Topics learned in later sections

  1. Numerical Value