Question

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

x f(x)
−1 -12
0 -6
1 0

g(x)
g(x) = 2x + 6


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

PART A)
if f(x) is a line, you can find this expression:

y = m * x + b

Substitute two values to find, m and b. m is the slope, b the intercept, OK?

(0,-6) ---> -6 = b, so b= -6.
(1, 0) ---> 0 = m + b = m - 6, m = 6.

f(x) = 6x-6.

Check it:

(-1,-12)? y = 6*(-1)-6 = -12, yeah!!!

Now, g(x) is written as slope-intercept already:

slope = 2 (the coefficient of x)
intercept = 6 (the term without x)

slope of f(x) =6, slope of g(x) = 2

PART B)

6>-6, so the intercept of g(x) is greater.

Hope you learned sth! :)