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A section of a hiking trail begins at the coordinates (-7, 5) and follows a straight path that ends at the coordinates (3, 9). What is the rate of change of the hiking trail?

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SaniShahbaz

Answer:

The rate of change of the hiking trail is [tex]m=\frac{2}{5}[/tex].

Step-by-step explanation:

  • A section of a hiking trail begins at the coordinates (-7, 5). It does mean (x₁, y₁) ⇒ (-7, 5)
  • And follows a straight path that ends at the coordinates (3, 9). It does mean (x₂, y₂) ⇒ (3, 9)

In mathematical language, the slope m of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Plugging (x₁, y₁) ⇒ (-7, 5) and  (x₂, y₂) ⇒ (3, 9) into the slope equation

[tex]m=\frac{9-5}{3-(-7)}[/tex]

[tex]m=\frac{4}{10}[/tex]

[tex]m=\frac{2}{5}[/tex]

So, the rate of change of the hiking trail is [tex]m=\frac{2}{5}[/tex].

Keywords: rate of change, slope, coordinates

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