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)

g(x) = 4x + 3



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)

Answer 1

First, lets solve f(x). g(x) is already given. Find the slope of f(x) by doing m = y2-y1/x2-x1. I'm going to use -1,-5 (1) and 0,-1 (2). -1-(-5) = 4 and 0-(-1) = 1. This means that the slope is 4 since 4/1 = 4.
Now find y intercept (b). Since we know that y=4x+b, we can solve this by plugging in an ordered pair. I will use -1,-5. -5 = 4(-1) +b. With this, we see that -5 = -4+b and b = -1 since -5 = -4-1.
Your equation for f(x) is y=4x-1.
A: The slopes are equal since both of them are 4.
B: g(x) has a greater y intercept since 3 > -1.