Math Problem Statement

Which statement is true regarding the slope of Function A and Function B?

Solution

We are given two functions:

  • Function A is defined by a table of values: \hline x & y \\ \hline -8 & 1 \\ -4 & 2 \\ 8 & 5 \\ \hline \end{array}$$
  • Function B is y=x+3y = x + 3, where the slope is clearly 1.

Now, let's calculate the slope of Function A using the slope formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Let's take two points from the table, say (8,1)(-8, 1) and (4,2)(-4, 2): m=214(8)=14m = \frac{2 - 1}{-4 - (-8)} = \frac{1}{4}

Thus, the slope of Function A is 14\frac{1}{4}.

Since the slope of Function B is 1, and 14<1\frac{1}{4} < 1, the slope of Function A is less than the slope of Function B.

So, the correct answer is:

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

Would you like more details or have any questions?

Here are 5 related questions to further explore:

  1. How do you determine the slope of a line from a graph?
  2. Can the slope of a linear function be zero?
  3. What does a negative slope indicate in a linear function?
  4. How would you graph Function B using its equation?
  5. What is the meaning of the slope in real-world problems?

Tip: The slope of a line tells you how steep the line is and whether it rises or falls as you move from left to right on a graph.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Slope
Algebra

Formulas

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

Theorems

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Suitable Grade Level

Grades 8-10