Calculate Slope of Linear Function: Points A(2,10) to B(-5,-4)

Q: Why is the slope positive when both differences are negative?

Great observation! When you divide two negative numbers, you get a positive result. $ \frac{-14}{-7} = +2 $ because negative ÷ negative = positive.

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

No! You can choose either point as your starting point. Just make sure to stay consistent - if A is (x₁, y₁), then B must be (x₂, y₂) throughout your calculation.

Q: How can I tell if my slope makes sense by looking at the graph?

Look at the line's direction! A positive slope means the line goes up from left to right. Since point A(2,10) is higher than B(-5,-4), and A is to the right of B, the line rises = positive slope ✓

Q: What if I get a fraction instead of a whole number?

That's completely normal! Many slopes are fractions. Just simplify the fraction to lowest terms. For example, $ \frac{6}{9} = \frac{2}{3} $.

Q: Can slope ever be zero or undefined?

Yes! Slope is zero for horizontal lines (same y-values) and undefined for vertical lines (same x-values). But that doesn't happen with points A(2,10) and B(-5,-4).

Slope Formula with Negative Coordinates

In the drawing of the graph of the linear function passing through the points $A(2,10)$ y $B(-5,-4)$

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 We'll find the slope using 2 points

00:17 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 to find 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 $A(2,10)$ y $B(-5,-4)$

Find the slope of the graph.

Step-by-step solution

To find the slope of the graph of the linear function passing through points $A(2,10)$ and $B(-5,-4)$ , we use the slope formula:

The slope formula is given by:

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

Substitute $(x_1, y_1) = (2, 10)$ and $(x_2, y_2) = (-5, -4)$ :

$m = \frac{-4 - 10}{-5 - 2}$

Calculate the differences:

$y_2 - y_1 = -4 - 10 = -14$

$x_2 - x_1 = -5 - 2 = -7$

Substitute these into the slope formula:

$m = \frac{-14}{-7}$

Simplify:

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

Therefore, the slope of the graph is $2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Slope Formula: Use m = (y₂ - y₁)/(x₂ - x₁) for any two points
Technique: Calculate (-4 - 10)/(-5 - 2) = -14/-7 = 2
Check: Rise over run: up 14 units, right 7 units gives 14/7 = 2 ✓

Common Mistakes

Avoid these frequent errors

Mixing up coordinate order in subtraction
Don't subtract y₁ - y₂ and x₁ - x₂ = wrong sign! This flips the slope's direction completely. Always subtract consistently: (y₂ - y₁)/(x₂ - x₁) or use the same point order for both numerator and 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

Why is the slope positive when both differences are negative?

Great observation! When you divide two negative numbers, you get a positive result. $\frac{-14}{-7} = +2$ because negative ÷ negative = positive.

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

No! You can choose either point as your starting point. Just make sure to stay consistent - if A is (x₁, y₁), then B must be (x₂, y₂) throughout your calculation.

How can I tell if my slope makes sense by looking at the graph?

Look at the line's direction! A positive slope means the line goes up from left to right. Since point A(2,10) is higher than B(-5,-4), and A is to the right of B, the line rises = positive slope ✓

What if I get a fraction instead of a whole number?

That's completely normal! Many slopes are fractions. Just simplify the fraction to lowest terms. For example, $\frac{6}{9} = \frac{2}{3}$ .

Can slope ever be zero or undefined?

Yes! Slope is zero for horizontal lines (same y-values) and undefined for vertical lines (same x-values). But that doesn't happen with points A(2,10) and B(-5,-4).

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Calculate Slope of Linear Function: Points A(2,10) to B(-5,-4)

Slope Formula with Negative Coordinates

❤️ 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 positive when both differences are negative?

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

How can I tell if my slope makes sense by looking at the graph?

What if I get a fraction instead of a whole number?

Can slope ever be zero or undefined?

🌟 Unlock Your Math Potential

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