Linear Function Through Points (0,5) and (6,5): Analyzing Horizontal Lines

Q: What's the difference between zero slope and undefined slope?

Zero slope means the line is horizontal (flat) - like $ y = 5 $. Undefined slope means the line is vertical (straight up and down) - like $ x = 3 $.

Q: How do I know if a line is a constant function?

Check if all the y-values are the same! If points like (0,5) and (6,5) have identical y-coordinates, then y always equals that same number - making it constant.

Q: Why is the slope zero when both y-values are 5?

Because slope measures vertical change over horizontal change. When y-values don't change (5 to 5), the vertical change is 0, so $ \frac{0}{6} = 0 $!

Q: What does a constant function look like on a graph?

A constant function appears as a perfectly horizontal line. No matter how far left or right you go, the height (y-value) stays exactly the same.

Q: Can I have a constant function with any y-value?

Yes! Constant functions can be $ y = 5 $, $ y = -2 $, $ y = 0 $, or any number. The key is that y never changes regardless of the x-value.

Horizontal Lines with Zero Slope

The graph of the linear function passes through the points $B(0,5),A(6,5)$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The graph of the linear function passes through the points $B(0,5),A(6,5)$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify the points given: $B(0,5)$ and $A(6,5)$ .
Step 2: Use the slope formula to calculate the slope $m$ between these points:

The slope $m$ is calculated as:

m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 5}{6 - 0} = \frac{0}{6} = 0

Since the slope $m = 0$ , the line is horizontal.

Step 3: Classify the line as a "constant function" because the slope is zero, indicating no increase or decrease.

The line is therefore a constant function where the $y$ -value remains at 5 for all $x$ -values.

Therefore, the answer is constant function.

Final Answer

Constant function

Key Points to Remember

Essential concepts to master this topic

Slope Formula: When y-values are equal, slope equals zero
Technique: Calculate $m = \frac{5-5}{6-0} = \frac{0}{6} = 0$
Check: Horizontal line means constant y-value for all x-values ✓

Common Mistakes

Avoid these frequent errors

Confusing horizontal and vertical lines
Don't think horizontal lines have undefined slope = vertical line properties! Horizontal lines have zero slope (flat), while vertical lines have undefined slope. Always remember: horizontal = zero slope, vertical = undefined slope.

Practice Quiz

Test your knowledge with interactive questions

What is the solution to the following inequality?

$$ 10x-4\leq-3x-8 $$

FAQ

Everything you need to know about this question

What's the difference between zero slope and undefined slope?

Zero slope means the line is horizontal (flat) - like $y = 5$ . Undefined slope means the line is vertical (straight up and down) - like $x = 3$ .

How do I know if a line is a constant function?

Check if all the y-values are the same! If points like (0,5) and (6,5) have identical y-coordinates, then y always equals that same number - making it constant.

Why is the slope zero when both y-values are 5?

Because slope measures vertical change over horizontal change. When y-values don't change (5 to 5), the vertical change is 0, so $\frac{0}{6} = 0$ !

What does a constant function look like on a graph?

A constant function appears as a perfectly horizontal line. No matter how far left or right you go, the height (y-value) stays exactly the same.

Can I have a constant function with any y-value?

Yes! Constant functions can be $y = 5$ , $y = -2$ , $y = 0$ , or any number. The key is that y never changes regardless of the x-value.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime