Question

A function has an initial value of −1 and a slope equal to 3. Choose the sketch of a graph that exhibits the qualitative features of the function.
A. A coordinate plane with four quadrants shows the x and y axes ranging from negative 8 to 8 in increments of 1. An upward line with arrows on both the ends passes through the first, second, and third quadrants. The line intersects the x-axis at (-1, 0) and the y-axis at (0 comma 3).
B. A coordinate plane with four quadrants shows the x and y axes ranging from negative 8 to 8 in increments of 1. An upward line with arrows on both the ends passes through the first, fourth, and third quadrants. The line intersects the x-axis at (3, 0) and the y-axis at (0, -1).
C. A coordinate plane with four quadrants shows the x and y axes ranging from negative 8 to 8 in increments of 1. A downward line with arrows on both the ends passes through the second, first, and fourth quadrants. The line intersects the x-axis at (3, 0) and the y-axis at (0, 3).
D. A coordinate plane with four quadrants shows the x and y axes ranging from negative 8 to 8 in increments of 1. An upward line with arrows on both the ends passes through the first, fourth, and third quadrants. The line intersects the x-axis at (0.3, 0) and the y-axis at (0, -1).

Answer 1

D

Reason: "Initial value −1" means y-intercept (0, −1). Slope 3 gives equation y = 3x − 1, whose x-intercept is x = 1/3 ≈ 0.3. Option D shows (0, −1) and (0.3, 0) with an upward slope.