Calculate Slope Between Points A(1,7) and D(8,2): Linear Function Analysis

Q: Why is my slope negative?

A negative slope means the line goes downward from left to right. Since point A(1,7) is higher than point D(8,2), the line falls as x increases, giving you $ -\frac{5}{7} $.

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(1,7) is (x₁,y₁), then D(8,2) must be (x₂,y₂) throughout the calculation.

Q: How do I know if I calculated correctly?

Check your arithmetic: $ \frac{2-7}{8-1} = \frac{-5}{7} $. Also, since point A is above and to the left of point D, the slope should be negative.

Q: Can I simplify this fraction further?

No, $ -\frac{5}{7} $ is already in lowest terms because 5 and 7 share no common factors other than 1.

Q: What does the slope -5/7 mean in real terms?

For every 7 units you move right, the line goes 5 units down. The negative sign indicates the downward direction.

Slope Calculation with Negative Results

In the drawing of the graph of the linear function passing through the points $A(1,7)$ y $D(8,2)$

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 the 2 points

00:14 We'll use the formula to find the slope using 2 points

00:25 We'll substitute appropriate values according to the given data and solve for the slope

00:43 And this is the solution to the question

Step-by-step written solution

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Understand the problem

In the drawing of the graph of the linear function passing through the points $A(1,7)$ y $D(8,2)$

Find the slope of the graph.

Step-by-step solution

To find the slope of the linear function passing through the points $A(1,7)$ and $D(8,2)$ , we will use the formula for the slope between two points:

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

Let us assign the coordinates $(x_1, y_1) = (1, 7)$ and $(x_2, y_2) = (8, 2)$ .

Substitute these values into the slope formula:

$m = \frac{2 - 7}{8 - 1}$

Calculate the differences in the numerator and the denominator:

$m = \frac{-5}{7}$

Therefore, the slope of the line passing through points $A(1,7)$ and $D(8,2)$ is $-\frac{5}{7}$ .

In conclusion, the correct answer is $-\frac{5}{7}$ .

Final Answer

$-\frac{5}{7}$

Key Points to Remember

Essential concepts to master this topic

Slope Formula: Use m = (y₂ - y₁)/(x₂ - x₁) for any two points
Technique: Substitute A(1,7) and D(8,2): m = (2-7)/(8-1) = -5/7
Check: Negative slope means line goes down from left to right ✓

Common Mistakes

Avoid these frequent errors

Switching coordinates in the slope formula
Don't mix up which point is (x₁,y₁) and which is (x₂,y₂) = wrong sign in your answer! This happens when you use (8,2) first but then subtract (1,7) second. Always keep the same point order: if A(1,7) is first, use 1 as x₁ and 7 as y₁ throughout.

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 my slope negative?

A negative slope means the line goes downward from left to right. Since point A(1,7) is higher than point D(8,2), the line falls as x increases, giving you $-\frac{5}{7}$ .

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(1,7) is (x₁,y₁), then D(8,2) must be (x₂,y₂) throughout the calculation.

How do I know if I calculated correctly?

Check your arithmetic: $\frac{2-7}{8-1} = \frac{-5}{7}$ . Also, since point A is above and to the left of point D, the slope should be negative.

Can I simplify this fraction further?

No, $-\frac{5}{7}$ is already in lowest terms because 5 and 7 share no common factors other than 1.

What does the slope -5/7 mean in real terms?

For every 7 units you move right, the line goes 5 units down. The negative sign indicates the downward direction.

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Calculate Slope Between Points A(1,7) and D(8,2): Linear Function Analysis

Slope Calculation with Negative Results

❤️ 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 my slope negative?

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

How do I know if I calculated correctly?

Can I simplify this fraction further?

What does the slope -5/7 mean in real terms?

🌟 Unlock Your Math Potential

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