Question

An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows at both ends passes through the following closed points: (-4, -10/3), and (- 1, -4/3).
Determine the initial value and the rate of change of the linear function as given in the graph.
A. The initial value is 1/6, and the rate of change is 3/2.
B. The initial value is −2/3, and the rate of change is 2/3.
C. The initial value is 2/3, and the rate of change is −2/3.
D. The initial value is −2, and the rate of change is 2/3.

Answer 1

Slope = (−4/3 − (−10/3))/(−1 − (−4)) = (6/3)/3 = 2/3.
Use y = mx + b with (−1, −4/3): −4/3 = (2/3)(−1) + b → b = −4/3 + 2/3 = −2/3.

Initial value = −2/3, rate of change = 2/3 → B.