To find the slope of the equation, we can use the formula for slope (m):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this scenario, we have:
- \( (x_1, y_1) = (1 \text{ hour}, 100 \text{ feet}) \)
- \( (x_2, y_2) = (5 \text{ hours}, 360 \text{ feet}) \)
Substituting these values into the slope formula:
\[ m = \frac{360 - 100}{5 - 1} = \frac{260}{4} = 65 \]
Now that we have the slope \( m = 65 \), we can use the point-slope form of the equation of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
We can use either point. Using the first point \( (1, 100) \):
\[ y - 100 = 65(x - 1) \]
Alternatively, using the second point \( (5, 360) \):
\[ y - 360 = 65(x - 5) \]
Both forms are valid and describe the same line, but let's analyze the options:
- a. \( y - 360 = 65(x - 1) \) – Incorrect (point used incorrectly)
- b. \( y - 100 = 65(x - 5) \) – Incorrect (point used incorrectly)
- c. \( y - 100 = 260(x - 1) \) – Incorrect (wrong slope used)
- d. \( y - 360 = 65(x - 5) \) – Correct (valid point and correct slope)
Thus, the correct answer is:
d. 65; y - 360 = 65 (x - 5)