Identify the Function: Which Equation Matches This Graph?

Q: How do I tell if a line is horizontal?

A line is horizontal if it runs left to right without going up or down. It stays at the same height across the entire graph!

Q: What's the difference between y = 3 and y = 3x?

$ y = 3 $ is a horizontal line at height 3, while $ y = 3x $ is a slanted line that goes up 3 units for every 1 unit right.

Q: How do I find the equation of any horizontal line?

Just look at the y-coordinate where the line crosses the y-axis. If it crosses at y = 5, the equation is $ y = 5 $. Simple as that!

Q: Can horizontal lines have fractions in their equations?

Absolutely! You might see equations like $ y = \frac{1}{2} $ or $ y = -2.5 $. The line just sits at that fractional or decimal height.

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

Watch the teacher solve the problem with clear explanations

00:06 Let's find the right equation for the function shown in the graph.

00:09 First, we need to figure out the slope of this graph.

00:14 Choose two points on the graph to help us determine the slope.

00:22 Now, we'll use a formula to calculate the slope of the function.

00:26 Substitute the values from the graph into the formula, and let's find the slope.

00:33 Great! This is the slope of the graph.

00:39 Next, we'll use the linear equation format.

00:43 Put in the known values to calculate B, the Y-intercept.

00:48 Now, find the Y-intercept value, which is B.

00:52 This is the value of B, also known as the Y-intercept.

00:56 Let's put it all together to form the complete linear equation.

01:00 And there you have it! That's how we solve this problem.

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 determine the correct equation from the given choices, we observe that the graph represents a horizontal line, positioned at $y = 3$ . A horizontal line is defined by a constant y-value because it does not change as x changes. Thus, the line corresponds to the equation $y = 3$ , indicating this is the correct equation from the choices provided.

Therefore, the solution to the problem is $y = 3$ .

Final Answer

$y=3$

Key Points to Remember

Essential concepts to master this topic

Rule: Horizontal lines have constant y-values for all x-values
Technique: Identify y-coordinate where line crosses y-axis: y = 3
Check: Pick any x-value and verify y stays 3 ✓

Common Mistakes

Avoid these frequent errors

Confusing horizontal and vertical lines
Don't think horizontal lines depend on x like y = 3x = wrong slope! This creates a slanted line instead of horizontal. Always remember horizontal lines have zero slope and equation 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 do I tell if a line is horizontal?

A line is horizontal if it runs left to right without going up or down. It stays at the same height across the entire graph!

What's the difference between y = 3 and y = 3x?

$y = 3$ is a horizontal line at height 3, while $y = 3x$ is a slanted line that goes up 3 units for every 1 unit right.

Why doesn't x appear in the equation y = 3?

Because the y-value never changes! No matter what x-value you pick, y will always equal 3. The x has no effect on the y-value.

How do I find the equation of any horizontal line?

Just look at the y-coordinate where the line crosses the y-axis. If it crosses at y = 5, the equation is $y = 5$ . Simple as that!

Can horizontal lines have fractions in their equations?

Absolutely! You might see equations like $y = \frac{1}{2}$ or $y = -2.5$ . The line just sits at that fractional or decimal height.

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