Math Problem Statement

Which statement is true: The slope of Function A is greater or less than the slope of Function B?

Solution

Let's begin by calculating the slopes of both Function A and Function B to determine which statement is true.

Function A:

The slope of a linear function can be calculated using the formula:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

From the table, we can choose two points from Function A: (9,7)and(6,4)(-9, -7) \quad \text{and} \quad (-6, -4)

Now, plug the values into the slope formula: mA=4(7)6(9)=4+76+9=33=1m_A = \frac{-4 - (-7)}{-6 - (-9)} = \frac{-4 + 7}{-6 + 9} = \frac{3}{3} = 1

So, the slope of Function A is mA=1m_A = 1.

Function B:

From the graph of Function B, we can pick two points: (0,8)and(2,2)(0, -8) \quad \text{and} \quad (2, -2)

Using the same slope formula: mB=2(8)20=2+820=62=3m_B = \frac{-2 - (-8)}{2 - 0} = \frac{-2 + 8}{2 - 0} = \frac{6}{2} = 3

So, the slope of Function B is mB=3m_B = 3.

Comparison:

Since mA=1m_A = 1 and mB=3m_B = 3, the slope of Function A is less than the slope of Function B.

Thus, the correct statement is:

The slope of Function A is less than the slope of Function B.\boxed{\text{The slope of Function A is less than the slope of Function B.}}

Would you like more details or explanations? Here are some follow-up questions that might help:

  1. How does the slope affect the steepness of a line?
  2. Can you explain how to find the slope between two points in general?
  3. How do changes in the slope value influence the direction of a line?
  4. Can you derive the equation of the line for Function A or B from this information?
  5. What are other ways to represent linear functions besides slope-intercept form?

Tip: The greater the absolute value of a slope, the steeper the line. A positive slope means the line rises as it moves to the right, while a negative slope means it falls.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Slope

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

Slope of a Line Theorem

Suitable Grade Level

Grades 8-10