Calculate the Slope: Linear Function Through Points (-3,2) and (3,2)

Q: What's the difference between slope 0 and undefined slope?

Slope 0: Horizontal line (same y-values)Undefined slope: Vertical line (same x-values). Remember: you can't divide by zero, so vertical lines have no slope value.

Q: How can I visualize this on the graph?

Look at the points A(-3,2) and B(3,2). They're both at height 2 on the y-axis! This creates a perfectly horizontal line, which always has slope = 0.

Q: What if the points were at different y-values?

If A(-3,1) and B(3,3), then slope = $ \frac{3-1}{3-(-3)} = \frac{2}{6} = \frac{1}{3} $The line would be slanted upward instead of horizontal

Slope Calculation with Horizontal Lines

In the drawing of the graph of the linear function passing through the points $A(-3,2)$ y $B(3,2)$

Find the slope of the graph.

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Step-by-step video solution

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00:00 Find the slope of the graph

00:04 Let's find the slope using 2 points

00:19 We'll use the formula to find the slope using 2 points

00:28 We'll substitute appropriate values according to the given data and solve for the slope

00:44 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

In the drawing of the graph of the linear function passing through the points $A(-3,2)$ y $B(3,2)$

Find the slope of the graph.

Step-by-step solution

To determine the slope of the line passing through points $A(-3, 2)$ and $B(3, 2)$ , we will use the slope formula:

The slope $m$ is calculated as:

m = \frac{y_2 - y_1}{x_2 - x_1}

Substituting the values from points $A(-3, 2)$ and $B(3, 2)$ , we get:

m = \frac{2 - 2}{3 - (-3)} = \frac{0}{6} = 0

The calculation shows that the difference in $y$ -coordinates is zero, hence dividing by any non-zero number will result in a slope of zero. This indicates a horizontal line on the graph.

Therefore, the slope of the line is $0$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Slope equals change in y divided by change in x
Technique: $m = \frac{2-2}{3-(-3)} = \frac{0}{6} = 0$
Check: Same y-coordinates mean horizontal line with slope zero ✓

Common Mistakes

Avoid these frequent errors

Confusing horizontal and vertical lines
Don't think horizontal lines have undefined slope = wrong answer! Horizontal lines have the same y-coordinate, so the numerator is zero, giving slope = 0. Always remember: horizontal lines have slope 0, vertical lines have 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

Why is the slope 0 and not undefined?

The slope is 0 because both points have the same y-coordinate (2). When you calculate $\frac{2-2}{3-(-3)} = \frac{0}{6} = 0$ , you get zero. Undefined slope only happens when dividing by zero (vertical lines).

What's the difference between slope 0 and undefined slope?

Slope 0: Horizontal line (same y-values)
Undefined slope: Vertical line (same x-values). Remember: you can't divide by zero, so vertical lines have no slope value.

How can I visualize this on the graph?

Look at the points A(-3,2) and B(3,2). They're both at height 2 on the y-axis! This creates a perfectly horizontal line, which always has slope = 0.

Does it matter which point I call (x₁,y₁)?

No! Whether you use A as point 1 or point 2, you'll get the same answer. Try it: $\frac{2-2}{-3-3} = \frac{0}{-6} = 0$ . The slope is still 0!

What if the points were at different y-values?

If A(-3,1) and B(3,3), then slope = $\frac{3-1}{3-(-3)} = \frac{2}{6} = \frac{1}{3}$
The line would be slanted upward instead of horizontal

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Calculate the Slope: Linear Function Through Points (-3,2) and (3,2)

Slope Calculation with Horizontal Lines

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the slope 0 and not undefined?

What's the difference between slope 0 and undefined slope?

How can I visualize this on the graph?

Does it matter which point I call (x₁,y₁)?

What if the points were at different y-values?

🌟 Unlock Your Math Potential

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