Question

Determine which expression(s) best describes the function, ƒ(x ) = 1/3 x - 1. Choose all that apply.

The function has a y-intercept of (0, -1).
Given any two coordinates that lie on the graph of the function, the Pythagorean Theorem can be used to determine the midpoint of the function.
The slope is sometimes consistent for any pair of coordinates that lie on the graph of the function.
For a right triangle with a vertical side length of 1 unit and a horizontal side length of 3 units, if one point of the hypotenuse of the triangle is on the graph of the function, then so is the other.
The function has an x-intercept of (3, 0).

Answer 1

Correct choices: 1, 4, and 5.

Explanations:
- (0, −1) is the y-intercept since f(0) = (1/3)(0) − 1 = −1.
- For a right triangle with vertical side 1 and horizontal side 3 the rise/run = 1/3, which matches the line’s slope, so if one hypotenuse endpoint lies on the line the other does too.
- The x-intercept is (3, 0) because (1/3)x − 1 = 0 ⇒ x = 3.

Why the others are wrong:
- The Pythagorean Theorem gives distances, not midpoints; the midpoint uses averages ((x1+x2)/2, (y1+y2)/2).
- The statement “The slope is sometimes consistent for any pair…” is incorrectly worded. The slope of a line is consistent (always the same) for any pair of distinct points — so the phrase “sometimes” makes the statement false as written.