Question

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)

Answer 1

Answer:

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

B)  g(x) has the greater y-intercept

Step-by-step explanation:

Part A - Slopes

Function f(x)

Choose two ordered pairs from the given table:

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

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

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

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

Answer 2

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