Math Problem Statement

What is the rate of change of the linear function? Simplify your final answer and type as a fraction if necessary.

What is the rate of change of the linear function? Simplify your final answer and type as a fraction if necessary.

Solution

To find the rate of change (or slope) of the linear function, we can use two points on the line and apply the slope formula:

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

From the graph, I can identify two points that the line passes through:

  • Point 1: (2,0)(-2, 0)
  • Point 2: (2,4)(2, 4)

Now, let's calculate the slope mm:

m=402(2)=44=1m = \frac{4 - 0}{2 - (-2)} = \frac{4}{4} = 1

So, the rate of change of the linear function is 11.

Would you like more details, or do you have any questions?

Here are some related questions you might find helpful:

  1. What is the equation of the line using the slope-intercept form?
  2. How do you find the y-intercept of a linear function from a graph?
  3. What does the slope of a linear function represent in real-world problems?
  4. Can the slope of a line be negative? If so, what does that indicate?
  5. How do you find the slope between two points algebraically without a graph?

Tip: The slope of a line indicates how much yy changes for a unit change in xx. A positive slope means the line is increasing, while a negative slope indicates a decreasing line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Slope Calculation

Formulas

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

Theorems

Linear function properties
Slope of a line

Suitable Grade Level

Grades 7-9