Question

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

Answer 1

Answer:

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

Step-by-step 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