40 POINTS Question 5(Multiple Choice Worth 4 points)

(07.04A)

The graph represents function 1, and the equation represents function 2:

Function 1
A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 6.

Function 2
y = 2x + 7

How much more is the rate of change of function 2 than the rate of change of function 1?

1
2
3
4

2

Step-by-step explanation:

Linear equation form:  y = mx + b

(where m is the slope and b is the y-intercept)

The rate of change for a line is the slope.

Function 1:  y = 6

⇒ the slope is zero so the rate of change is zero

Function 2:  y = 2x + 7

⇒ the slope is 2 so the rate of change is 2

Therefore, 2 - 0 = 2

So the rate of change of function 2 is 2 more than the rate of change of function 1

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

the answer is 13/48

step-by-step explanation: