Question

The equation below represents Function A and the graph represents Function B:

Function A

f(x) = – 2x + 1

Function B

graph of line going through ordered pairs negative 1, negative 5 and 2, 1 and 3, 3

Which equation best compares the slopes of the two functions? (1 point)


Slope of Function B = 2 x Slope of Function A.

Slope of Function A = Slope of Function B

Slope of Function A = 2 x Slope of Function B

Slope of Function B = – Slope of Function A

Answer 1

Slope of Function B = – Slope of Function A

Explanation:

Slope of function A=
`-2`

Slope of function B=$\frac{3-1}{3-2}=2$

Answer 2

Slope of Function B = -Slope of Function A

Explanation:

To find the right answer we need to calcultate the slope of each function.

Function A is
`f(x)=-2x+1`

From its expression we can deduct that its slope is
`m_(A) =-2` because the function is expressed in slope-intercept form where the coefficient of the x is the slope.

Now, function B is defined with a graph line, that intercepts points (-1,-5), (2,1) and (3,3). Using this points we can find its slope using the formula

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) ) \\m_(B) =(3-(-5))/(3-(-1)) =(3+5)/(3+1)=(8)/(4)=2`

So, function A has a slope of -2 and function B has a slope of 2.

Therefore, the last choice compares both slopes, because they are just opposite,

`m_(B)=-m_(A)`

So, the answer is

Slope of Function B = -Slope of Function A