Question

Jeremy claims that if a linear function has a slope of the same steepness and the same y-intercept as the linear function in the graph, then it must be the same function.

On a coordinate plane, a line goes through points (0, negative 1) and (2, 0).

Which equation proves Jeremy’s argument is incorrect?
y = negative one-half x minus 1
y = negative one-half x + 1
y = one-half x minus 1
y = one-half x + 1

Answer 1

The given line goes through (0, −1) and (2, 0), so its equation is y = (1/2)x − 1 (slope 1/2, y‑intercept −1).

The equation y = −(1/2)x − 1 has the same steepness (|slope| = 1/2) and the same y‑intercept (−1) but is a different line (at x = 2 it gives y = −2, not 0).

So y = −1/2 x − 1 disproves Jeremy.