Math Problem Statement

What is the rate of change? Use the y-intercept and the highlighted dot.

Solution

To find the rate of change (or slope) from the graph, we will use the two points highlighted: the y-intercept and the other visible point.

Step-by-Step Process:

  1. Identify the coordinates of the points:

    • The y-intercept appears to be at (0,1200)(0, 1200) (where the line crosses the y-axis).
    • The second highlighted point appears to be at (60,1200)(60, -1200).
  2. Use the slope formula: slope=y2y1x2x1\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} Where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of the two points.

    Plugging in the values: slope=12001200600=240060=40\text{slope} = \frac{-1200 - 1200}{60 - 0} = \frac{-2400}{60} = -40

Final Answer:

The rate of change (or slope) is 40-40.

This means for every unit increase in xx, yy decreases by 40 units.

Would you like more details on this calculation or have any questions?

Here are 5 related questions you might explore:

  1. What is the equation of the line in slope-intercept form?
  2. How do you interpret a negative rate of change in a real-world scenario?
  3. How can you calculate the rate of change using different points on the line?
  4. What does it mean if the rate of change (slope) is zero?
  5. How would the graph look if the slope were positive?

Tip: When calculating the slope, always ensure you subtract the yy values in the same order as the xx values!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope

Formulas

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

Theorems

Slope-Intercept Form: y = mx + b

Suitable Grade Level

Grades 7-9