Line Through Points (3,6) and (10,20): Coordinate Geometry Problem

Q: Does it matter which point I call (x₁, y₁) and which I call (x₂, y₂)?

No, it doesn't matter! You can assign either point as the first or second. Just make sure to stay consistent - if (3,6) is your first point, use 3 as x₁ and 6 as y₁ throughout.

Q: How do I remember the slope formula?

Think "rise over run"! The rise is how much y changes $ (y_2 - y_1) $, and the run is how much x changes $ (x_2 - x_1) $.

Q: What if I get a fraction that doesn't simplify to a whole number?

That's perfectly fine! Many slopes are fractions like $ \frac{2}{3} $ or $ \frac{5}{4} $. Just make sure to simplify to lowest terms if possible.

Q: Can the slope be zero?

Yes! When y₂ = y₁, the numerator becomes zero, giving slope = 0. This means you have a horizontal line where y stays the same as x changes.

Q: What happens if x₂ = x₁?

Then you get division by zero, which means the slope is undefined! This happens with vertical lines where x stays the same but y changes.

Slope Formula with Two Given Points

The line passes through the points $(3,6),(10,20)$

❤️ Continue Your Math Journey!

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

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the slope of the graph

00:04 For each point, we'll mark X and Y

00:10 We'll use the formula to find the slope using 2 points on the graph

00:20 We'll substitute appropriate values according to the given data, and solve to find the slope

00:39 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

The line passes through the points $(3,6),(10,20)$

Step-by-step solution

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

Step 1: Identify and assign coordinates
Step 2: Apply the slope formula
Step 3: Simplify the calculations

Let's proceed with each step:

Step 1: Assign coordinates from the given points:
$(x_1, y_1) = (3, 6)$ and $(x_2, y_2) = (10, 20)$ .

Step 2: Apply the slope formula, which is:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20 - 6}{10 - 3}$ .

Step 3: Calculate the slope:

$m = \frac{14}{7} = 2$ .

Therefore, the slope of the line passing through the points $(3, 6)$ and $(10, 20)$ is $m = 2$ .

The correct choice from the given options is $m = 2$ .

Final Answer

$m=2$

Key Points to Remember

Essential concepts to master this topic

Slope Formula: Use m = (y₂ - y₁)/(x₂ - x₁) for any two points
Technique: Calculate differences: (20 - 6)/(10 - 3) = 14/7 = 2
Check: Verify slope is consistent between any two points on line ✓

Common Mistakes

Avoid these frequent errors

Mixing up coordinate order in slope formula
Don't subtract coordinates randomly like (x₁ - x₂)/(y₂ - y₁) = inconsistent result! This gives you the wrong slope or even undefined values. Always keep the same order: (y₂ - y₁) in numerator and (x₂ - x₁) in denominator.

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

Does it matter which point I call (x₁, y₁) and which I call (x₂, y₂)?

No, it doesn't matter! You can assign either point as the first or second. Just make sure to stay consistent - if (3,6) is your first point, use 3 as x₁ and 6 as y₁ throughout.

What if I get a negative slope?

Negative slopes are completely normal! They mean the line is decreasing (going down from left to right). Always double-check your subtraction to make sure the sign is correct.

How do I remember the slope formula?

Think "rise over run"! The rise is how much y changes $(y_2 - y_1)$ , and the run is how much x changes $(x_2 - x_1)$ .

What if I get a fraction that doesn't simplify to a whole number?

That's perfectly fine! Many slopes are fractions like $\frac{2}{3}$ or $\frac{5}{4}$ . Just make sure to simplify to lowest terms if possible.

Can the slope be zero?

Yes! When y₂ = y₁, the numerator becomes zero, giving slope = 0. This means you have a horizontal line where y stays the same as x changes.

What happens if x₂ = x₁?

Then you get division by zero, which means the slope is undefined! This happens with vertical lines where x stays the same but y changes.

🌟 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