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 $(3,6),(10,20)$

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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

Look at the linear function represented in the diagram.

When is the function positive?

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.

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