Question

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

x f(x)
−1 −7
0 −1
1 5
g(x)
g(x) = 5x − 4

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)

Answer 1

g(x) = y=5x-4

f(x) =. y= 6x-1

I know the slope of f(x) is greater than the slope of g(x) since the slope of f(x)=6 and g(x)=5 and 6>5.

I also know that the y-intercept of f(x) is greater because f(x)=-1 and g(x)=-4 and -1>-4.

Explanation:

First, I will put both functions into slope-intercept form.

Next, I will use by picking two points on the table. and

this equals or 6.

So, I know the slope is 6.

To find the y-intercept I have to do, -7=6(-1)+b

So, the y-intercept is -1.

From this, I know the slope of f(x) is greater than the slope of g(x) since the slope of f(x)=6 and g(x)=5 and 6>5.

I also know that the y-intercept of f(x) is greater because f(x)=-1 and g(x)=-4 and -1>-4.

Answer 2

A.

⇒The slope of the function f(x) is greater than the slope of the function g(x).

This is so because using the slope intercept form equation, the slope of f(x) is 6 while that of g(x) is 5

B.

⇒The function f(x) has a greater y-intercept than the function g(x)

⇒The y intercept for the function f(x) is -1 where as that of the function g(x) is -4

Explanation:

This question is on the standard equation of a linear function using the slope-intercept form

y=m x+c----------where m is the gradient/slope of the line and c is the y-intercept.

Given the values in function f(x) we can identify the points in the line as;

(-1,-7), (0,-1) , (1,5)............plot the points to obtain the graph as indicated in the attachment.

Find the gradient of the graph ;

m₁=Δy/Δx

m₁= 5--1/1-0 =6/1 =6

Equation of line will be;

y-5/x-1 = 6

y-5=6(x-1)

y-5=6x-6

y=6x-1.........................m₁=6 and c₁= -1

Given that;

g(x)=5x-4.........................m₂=5 c₂= -4

⇒The slope of slope of the function f(x) is greater than the slope of the function g(x).

This is so because using the slope intercept form equation, the slope of f(x) is 6 while that of g(x) is 5

B.

⇒The function f(x) has a greater y-intercept than the function g(x)

⇒The y intercept for the function f(x) is -1 where as that of the function g(x) is -4

In the attached graph;

Red line graph, y=5x-4

Blue line graph, y=6x-1