Q4. - Algebra 1

Question

Write an equation involving absolute value for the graph

Step-by-Step Solution

Answer

The absolute value for the graph  is $\left|x-22\right|=5$.

Step-1. Apply the concept of midpoint.

Midpoint: - Midpoint is calculated between two points. Let the points be a and b. Then midpoint will be the point in between them from which the distance of a and b are same.

Step-2. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Step-3. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means the positive value of that quantity.

Example: -

Consider a variable x. Here, x can be both positive or negative but $\left|x\right|$ will always be positive and hence the absolute value. 

Step-4. Solution of the given equation.

First, find the midpoint of the two given points on the graph, i.e.,.17 and 27.

Let the mid-point be c. Then,

$$\begin{gathered} c=\frac{17+27}{2} \\ =\frac{44}{2} \\ =22 \end{gathered}$$

The distance from 22 to 17 is 5 units and the distance from 22 to 27 is also 5 units.

Now consider a variable x, then the equation will be: $\left|x-22\right|=5$.

 

Hence, the required equation is $\left|x-22\right|=5$.