Question

The rule for Function A is y= -2/3x

The graph below represents Function B.


Which statements about the two functions are true?


Both functions have negative rates of change.

Both functions have the same rate of change.

When graphed, Function A and Function B are parallel.

Function B has a greater rate of change than Function A.

Answer 1

Answer:

Both functions have negative rates of change

Function B has a greater rate of change than Function A

Step-by-step explanation:

we know that

Function A

The rule for Function A is

$y=-\frac{2}{3}x$

This is the equation of a proportional relationship (the line passes through the origin)

The slope is equal to $m=-\frac{2}{3}$

Function B

Find the equation of the function B

we have the points (-2,0) and (0,-2)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{-2-0}{0+2}$

$m=\frac{-2}{2}$

$m=-1$

The equation of the function B in slope intercept form is equal to

$y=mx+b$

we have

$m=-1\\b=-2$

substitute

$y=-x-2$

Verify each statement

Option 1) Both functions have negative rates of change

The statement is true

Because, the rate of change is the slope of the linear equation

Function A ----> $m=-\frac{2}{3}$

Function B ----> $m=-1$

Option 2) Both functions have the same rate of change.

The statement is false (see the explanation)

The rate of change are different ( m=-2/3 and m=-1)

Option 3) When graphed, Function A and Function B are parallel

The statement is false

When graphed, Function A and Function B are intersecting lines, because their slopes are different

Option 4) Function B has a greater rate of change than Function A

The statement is true

Remember that the rate of change can be either positive (increasing function) or negative (decreasing function). To find out which function has a greater rate of change, compare the absolute value of their slopes

therefore

1 > 2/3