The table below represents a linear function f(x) and the equation represents a function g(x): Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

(10 points)

Step-by-step explanation:

Part A

for f(x) slope between points (-1,-6) and (1,0)

m= y2-y1/x2-x1 = -6-0/-1-1 = -6/-2= 3

for g(x) slope m=4 because we compare to equation y=mx+b the given equation g(x)=4x-5

The slope of f(x) is 3 and the slope g(x) is 4 so the line of g(x) is steeper

part B

The y intercept for g(x) is  (0, -5)

The equation of f(x) can be found

y-y1 =m(x-x1) take any point for example point (1,0)

y-1 =3(x-0)

y=3x+1 so the y-intercept is at (0,1)

The y-intercept for f(x) is greater at y=1 then the one of g(x) at y=-5

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