Math Problem Statement

Write the equation to represent the graph for Sara's typing progress in words over time.

Solution

To determine the equation that represents the graph, we need to examine the relationship between the variables on the graph, which shows Typed Words in Essay on the y-axis and Minutes on the x-axis.

  1. Identifying the slope (rate of change):
    We can observe that the graph has a straight line starting from the origin, which implies a proportional relationship. Let's calculate the slope by picking two points on the line. For instance:

    • At (4, 80): in 4 minutes, 80 words are typed.
    • At (8, 160): in 8 minutes, 160 words are typed.

    Slope m=ΔyΔx=1608084=804=20m = \frac{\Delta y}{\Delta x} = \frac{160 - 80}{8 - 4} = \frac{80}{4} = 20.

    So, the slope mm is 20, meaning Sara types 20 words per minute.

  2. Writing the equation:
    Since the line passes through the origin, the equation has the form y=mxy = mx. Substituting m=20m = 20: y=20xy = 20x

    where yy is the number of words typed, and xx is the time in minutes.

The equation representing the graph is: y=20xy = 20x

Would you like more details or have any questions about this solution?

Here are five related questions to explore further:

  1. How would the equation change if Sara typed faster, say 30 words per minute?
  2. How can we determine if a relationship is proportional just by looking at a graph?
  3. What would the y-intercept represent if the line didn’t start at the origin?
  4. How would we calculate the total words typed in a specific number of minutes, like 15 minutes, using this equation?
  5. If Sara took a break and resumed typing, how would that appear on the graph?

Tip: In proportional relationships, the graph always passes through the origin (0,0) and has a constant slope, representing the rate.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Proportional Relationships

Formulas

y = mx

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 6-8