Identify the Matching Equation: Analyze the Graph Function Representation

Q: How can I tell if a line is horizontal just by looking at the graph?

A horizontal line runs left to right and is parallel to the x-axis. It never goes up or down - it stays at the same height (y-value) no matter what x-value you choose.

Q: Why doesn't the equation include x?

Because the y-value never changes! No matter what x-value you pick, y will always equal -2. Since y doesn't depend on x, we don't need x in the equation.

Q: What's the difference between y = -2 and x = -2?

$ y = -2 $ is a horizontal line crossing the y-axis at -2. $ x = -2 $ is a vertical line crossing the x-axis at -2. They're completely different!

Q: How do I find the slope of a horizontal line?

Horizontal lines have a slope of 0 because they don't rise or fall. The slope formula gives us $ \frac{\text{rise}}{\text{run}} = \frac{0}{\text{any number}} = 0 $.

Q: Can a horizontal line pass through any point?

Yes! For any point $ (a, b) $, there's exactly one horizontal line passing through it: $ y = b $. The x-coordinate doesn't matter for the equation.

Horizontal Lines with Constant Functions

Which of the following equations corresponds to the function represented in the graph?

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Step-by-step video solution

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00:00 Find the appropriate equation for the function in the graph

00:04 We want to find the slope of the graph

00:08 Let's take 2 points on the graph

00:13 We'll use the formula to find the function graph's slope

00:17 We'll substitute appropriate values according to the given data and solve to find the slope

00:22 This is the slope of the graph

00:27 We'll use the linear equation

00:31 We'll substitute appropriate values and solve to find B

00:39 This is the value of B (intersection point with Y-axis)

00:42 We'll construct the linear equation using the values we found

00:46 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which of the following equations corresponds to the function represented in the graph?

Step-by-step solution

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

Step 1: Identify the type of line
The graph illustrates a horizontal line at $y = -2$ . Horizontal lines have a constant y-value across all x-values.
Step 2: Recognize the equation of the line
A horizontal line has the form $y = c$ , where $c$ is a constant. Here, $c = -2$ .
Step 3: Match with given options
Among the given choices, $y = -2$ correctly represents the function for the graph as it shows a line intersecting the y-axis at -2 and running parallel to the x-axis.

Therefore, the solution to the problem is $y = -2$ , which corresponds to choice id "3".

Final Answer

$y=-2$

Key Points to Remember

Essential concepts to master this topic

Rule: Horizontal lines have equation form $y = c$ where c is constant
Technique: Find y-intercept: line crosses y-axis at $y = -2$
Check: Pick any x-value: when $x = 5$ , $y = -2$ ✓

Common Mistakes

Avoid these frequent errors

Confusing horizontal and vertical line equations
Don't write $x = -2$ for horizontal lines = vertical line equation! This describes a line parallel to the y-axis, not x-axis. Always remember horizontal lines have form $y =$ constant.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

FAQ

Everything you need to know about this question

How can I tell if a line is horizontal just by looking at the graph?

A horizontal line runs left to right and is parallel to the x-axis. It never goes up or down - it stays at the same height (y-value) no matter what x-value you choose.

Why doesn't the equation include x?

Because the y-value never changes! No matter what x-value you pick, y will always equal -2. Since y doesn't depend on x, we don't need x in the equation.

What's the difference between y = -2 and x = -2?

$y = -2$ is a horizontal line crossing the y-axis at -2. $x = -2$ is a vertical line crossing the x-axis at -2. They're completely different!

How do I find the slope of a horizontal line?

Horizontal lines have a slope of 0 because they don't rise or fall. The slope formula gives us $\frac{\text{rise}}{\text{run}} = \frac{0}{\text{any number}} = 0$ .

Can a horizontal line pass through any point?

Yes! For any point $(a, b)$ , there's exactly one horizontal line passing through it: $y = b$ . The x-coordinate doesn't matter for the equation.

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