107k views
4 votes
The table below represents a linear function f(x) and the equation represents a function g(x):

x f(x)
-1 -5
0 -1
1 3
g(x) = 4x + 3

Part A: Write a sentence to compare the slope of the two functions and show the steps you used to dete
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
(10 points)

User Fniessen
by
7.2k points

2 Answers

11 votes

Slope of f(x)

  • m=-1+5/0+1
  • m=4/1
  • m=4

slope of g(x)

  • m=4

Both have same slopes

Y intercept

  • f(x)=(0,-1)
  • g(x)=3

Hence g(x) has greater y intercept

User Lokesh Pandey
by
8.3k points
11 votes

Answer:

A) The slopes of the two functions are the same.

B) g(x) has the greater y-intercept

Explanation:

Part A - Slopes

Function f(x)

Choose two ordered pairs from the given table:


\textsf{let}\:(x_1,y_1)=(0,-1)


\textsf{let}\:(x_2,y_2)=(1,3)


\implies \sf \textsf{slope}\:(m)=(y_2-y_1)/(x_2-x_1)=(3-(-1))/(1-0)=4

Function g(x)

g(x) = 4x - 3

Slope-intercept form of a linear equation: y = mx + b

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

Therefore, the slope of g(x) is 4

The slopes of the two functions are the same.

Part B - y-intercepts

Function f(x)

Substitute one of the ordered pairs and the found slope from part A into the point-slope form of a linear equation to find the function f(x):


\implies y-y_1=m(x-x_1)


\implies y-(-1)=4(x-0)


\implies y=4x-1

Therefore, the y-intercept of f(x) is -1

Function g(x)

The y-intercept of g(x) is 3

Therefore, g(x) has the greater y-intercept as 3 > -1

User Matt Searles
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories