Question

the table below represents a linear function f(x) and the equation represents a function g(x):

x: -1 0 1
f(x): -9 -1 7
g(x)
g(x)=3x-2


Part A: write a sentence to compare the slope of the two functions and show the steps used to determine the slope of f(x) and g(x)

Part B: which function has a greater y-intercept? justify your answer.​

Answer 1

Answer:

On inspection of values of x and f(x) it is clear that f(x) is a linear function

i.e.

\begin{gathered}f(x) = x \\ \\\end{gathered}

f(x)=x

1)Slope of f(x) and y-intercept of f(x):

Convert the function in slope intercept form and calculate the slope.

Slope intercept form:

\begin{gathered}y = mx + C \\ \\\end{gathered}

y=mx+C

Here,

\begin{gathered}f(x) = x \\ \\ = > y = x \\ \\ = > y =1. x + 0.C \\ \\ = > \bold{\green{m = 1}} \\ \\\end{gathered}

f(x)=x

=>y=x

=>y=1.x+0.C

=>m=1

Slope of f(x)=1,

y-intercept of f(x)=(0,0)

2) Slope and y-intercept of g(x):

\begin{gathered}g(x) = 7x + 2 \\ \\ = > y = 7x + 2 \\ \\ \bold{\blue{m=7}}\end{gathered}

g(x)=7x+2

=>y=7x+2

m=7

Slope of g(x)=7

Y-INTERCEPT of g(x) =(0,2)

Part A:

Slope of f(x) is 1 and slope of g(x) is 7.

Part B:

g(x) has a greater y-intercept.

Hope it helps you.

To learn more on brainly:

1)find the slope of line x/3+y/2=1