Question

function a and function b are linear functions.
function a
(graph of function a: a line on a coordinate plane with x from -10 to 10 and y from -10 to 10, passing through some points)
function b

x	y
-4	12
-2	4
1	-8

function a and function b have different rates of change. using only integers, write the equation of another function whose slope is between those two rates of change.
y = \boxed{x} + \boxed{}

Explanation:

Step1: Find slope of Function A

From the graph, Function A passes through (0, 0) and (1, -6) (estimating from the line). Slope $m_A = \frac{-6 - 0}{1 - 0} = -6$.

Step2: Find slope of Function B

Using points (-4, 12) and (-2, 4) for Function B. Slope $m_B = \frac{4 - 12}{-2 - (-4)} = \frac{-8}{2} = -4$.

Step3: Determine a slope between -6 and -4

A slope between -6 and -4 is -5 (since -6 < -5 < -4).

Step4: Choose a y-intercept (any integer, let's pick 0 for simplicity)

The equation of a line is $y = mx + b$. With $m = -5$ and $b = 0$, the equation is $y = -5x + 0$.

Answer:

$y = \boxed{-5}x + \boxed{0}$ (Note: The y-intercept can be any integer, so other valid answers exist as long as the slope is between -6 and -4.)