Math Problem Statement

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

Solution

Let's analyze the question.

Function A is given as y=x4y = x - 4.
This is in slope-intercept form y=mx+by = mx + b, where mm is the slope. For Function A, the slope (mm) is 1.

For Function B, let's calculate the slope using the graph. The slope is the rise over the run:

  • From the graph, one point on Function B is (2,10)(-2, -10) and another is (2,10)(2, 10).
  • Rise = 10(10)=2010 - (-10) = 20, and Run = 2(2)=42 - (-2) = 4.
  • Slope = RiseRun=204=5\frac{\text{Rise}}{\text{Run}} = \frac{20}{4} = 5.

Thus:

  • The slope of Function A is 1.
  • The slope of Function B is 5.

Correct Answer:

The slope of Function A is less than the slope of Function B.

Would you like a detailed explanation of slope calculations?


Here are 5 related questions for practice:

  1. How do you find the slope of a line from two points?
  2. What is the y-intercept of Function A?
  3. How do you determine if two lines are parallel?
  4. Can you write the equation of Function B in slope-intercept form?
  5. How do you calculate the slope of a vertical or horizontal line?

Tip: Always remember, the slope is calculated as the ratio of vertical change (rise) to horizontal change (run).

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Slope

Formulas

Slope = (y2 - y1) / (x2 - x1)
y = mx + b (Slope-Intercept Form)

Theorems

Properties of Linear Functions

Suitable Grade Level

Grades 8-10