Math Problem Statement

What is the slope of the line? (Graph of Distance (miles) vs. Time (hours))

Solution

The slope of a line is determined by the formula:

slope=ΔyΔx\text{slope} = \frac{\Delta y}{\Delta x}

From the graph:

  • The yy-axis represents "Distance (miles)".
  • The xx-axis represents "Time (hours)".
  • At the point (0, 0), distance is 0 miles at 0 hours.
  • At the point (3, 60), distance is 60 miles at 3 hours.

Calculating the slope: slope=60030=603=20miles per hour (mi/h).\text{slope} = \frac{60 - 0}{3 - 0} = \frac{60}{3} = 20 \, \text{miles per hour (mi/h)}.

Thus, the correct answer is:

20 mi/h.

Would you like me to provide more details or explore a related topic?

Here are 5 related questions to consider:

  1. How do you calculate slope from a table of values?
  2. What are real-world examples of interpreting slopes?
  3. How does the slope change if the line is steeper or less steep?
  4. What is the meaning of a zero slope in a distance-time graph?
  5. How can you determine the slope if the graph scales change?

Tip: Always check units (e.g., miles, hours) when interpreting graphs!

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Math Problem Analysis

Mathematical Concepts

Linear Relationships
Slope Calculation
Interpreting Graphs

Formulas

slope = Δy / Δx

Theorems

Basic Slope Theorem

Suitable Grade Level

Grades 6-8