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

Slope Calculation with Negative Results

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

Find the slope of the graph.

A(1,7)A(1,7)A(1,7)CCCD(8,2)D(8,2)D(8,2)BBBxy

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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 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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1

Understand the problem

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

Find the slope of the graph.

A(1,7)A(1,7)A(1,7)CCCD(8,2)D(8,2)D(8,2)BBBxy

2

Step-by-step solution

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

m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1}

Let us assign the coordinates (x1,y1)=(1,7) (x_1, y_1) = (1, 7) and (x2,y2)=(8,2) (x_2, y_2) = (8, 2) .

Substitute these values into the slope formula:

m=2781 m = \frac{2 - 7}{8 - 1}

Calculate the differences in the numerator and the denominator:

m=57 m = \frac{-5}{7}

Therefore, the slope of the line passing through points A(1,7) A(1,7) and D(8,2) D(8,2) is 57-\frac{5}{7}.

In conclusion, the correct answer is 57-\frac{5}{7}.

3

Final Answer

57 -\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

Test your knowledge with interactive questions

What is the solution to the following inequality?

\( 10x-4≤-3x-8 \)

FAQ

Everything you need to know about this question

Why is my slope negative?

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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 57 -\frac{5}{7} .

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

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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?

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Check your arithmetic: 2781=57 \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?

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No, 57 -\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?

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

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