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

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For the function in front of you, the slope is?

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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