Math Problem Statement
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:
From the table, we can choose two points from Function A:
Now, plug the values into the slope formula:
So, the slope of Function A is .
Function B:
From the graph of Function B, we can pick two points:
Using the same slope formula:
So, the slope of Function B is .
Comparison:
Since and , the slope of Function A is less than the slope of Function B.
Thus, the correct statement is:
Would you like more details or explanations? Here are some follow-up questions that might help:
- How does the slope affect the steepness of a line?
- Can you explain how to find the slope between two points in general?
- How do changes in the slope value influence the direction of a line?
- Can you derive the equation of the line for Function A or B from this information?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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