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)

Answer 1

Question A:

Rewriting the table for f(x):

x      -1       0      1
f(x)   -7      -1      5

Notice that for every increase of one unit in 'x', there are an increase 6 units on f(x). Hence, the gradient of the slope of f(x) is 6. 

g(x) = 5x - 4 ⇒ This function follows the general form of the straight line equation, y = mx + c, where 'm' is the gradient and 'c' is the y-intercept.
Hence, the gradient of the slope of g(x) is 5.

The slope of f(x) is steeper than the slope of g(x).

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Question B:

The y-intercept is the value of y where a straight line crosses the y-axis (or when x is zero).

From the table of f(x), the y-intercept is -1 (this is the value of 'y' when 'x' is zero)

From the given function g(x) = 5x - 4, the y-intercept is -4. 

f(x) has a greater y-intercept.