Question

The table below represents a linear function f(x) and the equation represents a function g(x):. . . x. -1, 0, 1 ; f(x). -9, -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. (4 points)

Answer 1

The correct answers are:

Part A:  The slope of f(x) is greater; and Part B:  The y-intercept of f(x) is greater.

Explanation:

To find the slope of f(x), we use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1} \\ \\m=\frac{-1--9}{0--1}=\frac{-1+9}{0+1}=\frac{8}{1}=8$

The slope of g(x) is found in the form the function is written in, slope-intercept form; y=mx+b, where m is the slope and b is the y-intercept.  This means the slope of g(x) is 3.  Since the slope of f(x) is 8, the slope of f(x) is larger.

The y-intercept is the point where the data crosses the y-axis.  This means it will have an x-coordinate of 0.  The point in the table for f(x) with an x-coordinate of 0 is (0, -1).  This is the y-intercept of f(x).

The y-intercept of g(x) is b in the equation form y=mx+b.  For g(x), the y-intercept is -2.  -1 is greater than -2, so the y-intercept of f(x) is larger.

Answer 2

Slope of f(x) is [f(0) - f(-1)]/(0 - (-1)) = (-1 - (-9))/(0 + 1) = (-1 + 9)/1 = 8
equation of f(x) is (y - (-9))/(x - (-1)) = 8
(y + 9)/(x + 1) = 8
y + 9 = 8(x + 1) = 8x + 8
y = 8x - 1

The slope of f(x) is 8 while the slope of g(x) is 3.
The y-intercept of f(x) is -1 while that of g(x) is -2. Hence, f(x) has a greater y-intercept.