Question

On a coordinate plane, a parabola opens up. Solid circles appear on the parabola at (negative 6, 6), (negative 4. 5, 2. 25), (negative 3, 0), (negative 1. 5, negative 0. 75), (0, 0), (1,5, 2. 25), and (3, 6). Which is the rate of change for the interval between –6 and –3 on the x-axis?.

Answer 1

The rate of change for the interval between –6 and –3 on the x-axis is -2.

Given that

On a coordinate plane, a parabola opens up.

Solid circles appear on the parabola at (-6, 6), (-4. 5, 2. 25), (-3, 0), (-1. 5, -0. 75), (0, 0), (1,5, 2. 25), and (3, 6).

We have to determine

Which is the rate of change for the interval between –6 and –3 on the x-axis?

According to the question

On a coordinate plane, a parabola opens up.

Solid circles appear on the parabola at (-6, 6), (-4. 5, 2. 25), (-3, 0), (-1. 5, -0. 75), (0, 0), (1,5, 2. 25), and (3, 6).

The rate of change for the interval between x = -6 and x = -3 is simply asking you for the slope of the line that connects these 2 coordinates.

Then,

The rate of change for the interval between –6 and –3 on the x-axis is,

$\rm Rate \ of \ change = \dfrac{y_2-y_1}{x_2-x_1}\\ \\ Rate \ of \ change = \dfrac{-6-0}{-3-(-6)}\\ \\ Rate \ of \ change =\dfrac{-6}{3}\\ \\ Rate \ of \ change =-2$

Hence, the rate of change for the interval between –6 and –3 on the x-axis is -2.

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