Question

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

x f(x)
-1 -9
0 -1
1 7

g(x) = 3x - 2


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.

Answer 1

Part A: The slope of the linear function, f(x), equals 8, while the slope of g(x) = 3x - 2 equals 3.

--- Steps ---

Linear Function:

y2 - y1 -1 + 9
---------- = ---------- = 8
x2 - x2 0 + 1

g(x) = 3x - 2

Slope Intercept Form ~ y=mx+b
m is the slope, so in this equation, the slope is 3.

Part B: The function g(x) = 3x - 2 has a greater y intercept.

How to find the y intercepts:
g(x) = 3x - 2

The y intercept here is 2 because in slope intercept form, m is the slope and b is the y intercept: y =mx+b

F(x) table of values:

The y intercept here is -1. I found my answer by plotting all of the points on a coordinate grid. When you plot (0, -1), you will see that there is a spot where the line hits the y axis. That point is called the y intercept. So your y - value is -1, making the y intercept -1 also.

I hope this helps you out.