Calculate Slope of Linear Function: Points A(0,7) to B(8,-3)

Slope Calculation with Negative Values

In the drawing of the graph of the linear function passing through the points A(0,7) A(0,7) and
B(8,3) B(8,-3)

Find the slope of the graph.

A(0,7)A(0,7)A(0,7)B(8,-3)B(8,-3)B(8,-3)CCCxy

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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 We'll find the slope using 2 points
00:13 We'll use the formula to find the slope using 2 points
00:22 We'll substitute appropriate values according to the given data and solve for the slope
00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In the drawing of the graph of the linear function passing through the points A(0,7) A(0,7) and
B(8,3) B(8,-3)

Find the slope of the graph.

A(0,7)A(0,7)A(0,7)B(8,-3)B(8,-3)B(8,-3)CCCxy

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the coordinates of the points.

  • Step 2: Apply the slope formula.

  • Step 3: Perform the arithmetic to calculate the slope.

Let's work through each step:

Step 1: Identify the given points:
Point A A is (0,7) (0, 7) and Point B B is (8,3) (8, -3) .

Step 2: Use the slope formula, which is: m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1}

Substituting the coordinates of points A A and B B :
Here, (x1,y1)=(0,7) (x_1, y_1) = (0, 7) and (x2,y2)=(8,3) (x_2, y_2) = (8, -3) .

Step 3: Calculate the slope:
m=3780=108=54 m = \frac{-3 - 7}{8 - 0} \\ = \frac{-10}{8} \\ = -\frac{5}{4}

Therefore, the slope of the graph is 54 -\frac{5}{4} .

3

Final Answer

54 -\frac{5}{4}

Key Points to Remember

Essential concepts to master this topic
  • Formula: Use m = (y₂ - y₁)/(x₂ - x₁) for any two points
  • Technique: Calculate (-3 - 7)/(8 - 0) = -10/8 = -5/4
  • Check: Negative slope means line goes down from left to right ✓

Common Mistakes

Avoid these frequent errors
  • Switching coordinates or forgetting negative signs
    Don't mix up (x₁, y₁) and (x₂, y₂) or ignore negative values = wrong slope direction! This gives you 5/4 instead of -5/4, making your line go up instead of down. Always keep coordinates paired correctly and preserve all negative signs.

Practice Quiz

Test your knowledge with interactive questions

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

XY

FAQ

Everything you need to know about this question

Why is the slope negative?

+

The slope is negative because the line is falling from left to right. Point A(0,7) is higher up than point B(8,-3), so as x increases, y decreases, creating a negative slope.

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 do I simplify -10/8?

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Find the greatest common factor of 10 and 8, which is 2. Divide both numerator and denominator by 2: 108=54 \frac{-10}{8} = \frac{-5}{4}

What does slope -5/4 actually mean?

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It means for every 4 units you move right, the line drops down 5 units. The negative sign tells you the direction is downward.

Can I write -5/4 as a decimal?

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Yes! 54=1.25 -\frac{5}{4} = -1.25 . Both forms are correct, but fractions are often preferred in math class unless specifically asked for decimals.

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