Mathematics
Grade-8
Easy

Question

Which of the following would be a reasonable approximation for the length of time it would take this person to run 6 miles?

  1. ≅ 50 min
  2. ≅ 80 min
  3. ≅ 45 min
  4. ≅ 66 min

hintHint:

linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers.  A linear function represents a line, i.e., its graph is a line. Here,
  • 'm' is the slope of the line
  • 'b' is the y-intercept of the line
  • 'x' is the independent variable
  • 'y' (or f(x)) is the dependent variable

The correct answer is: ≅ 66 min


    linear function is of the form y = mx + b where 'm' and 'b' are real numbers.  A linear function represents a line, i.e., its graph is a line. Here,
    • 'm' is the slope of the line
    • 'b' is the y-intercept of the line
    • 'x' is the independent variable
    • 'y' (or f(x)) is the dependent variable

    Take any points from the graph
    (x1, y1) = (2, 20) and (x₂, y₂) = (5, 55).
    Step 1: Find the slope of the function using the slope formula:
    m = (y₂ - y1) / (x₂ - x1) = (55 - 20) / (5 - 2) = 35/3
    Step 2: Find the equation of linear function using the point slope form.
    y - y1 = m (x - x1)
    y - 20 = 35/3 (x - 2)
    y - 20 = 35/3 (x - 2)
    y  = 35/3(x) - 10/3
    for x = 6
    approximately equal to 66
    Thus, a reasonable approximation for the length of time it would take this person to run 6 miles is 66minutes.

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