Question

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

Answer 1

Part A:

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

$\frac{y_2 - y_1}{x_2 - x_1}$

Choose any two points from the table. We'll use (-1, -6) and (1, 0):

$\frac{0 - (-6)}{1 - (-1)} = \frac{6}{2} = 3$

The slope of f(x) is 3.

g(x) uses slope intercept form, which uses the following formula:

$y = mx + b$

m is the slope, and b is the y-intercept of the function.

g(x) is equal to 4x - 5. The coefficient for x is 4, which is the slope of the function. The slope is 4.

Compare the two slopes:

$\text{slope of f(x) = 3}$

$\text{slope of g(x) = 4}$

$3 < 4$

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

Part B:

The y-intercept is found when x is equal to 0.

f(x) already has a value for when x = 0: the y-value is -3.

g(x)'s y-intercept is found by the value of b in the function. The value of b in this function is -5.

Compare the two y-intercepts:

$\text{y-intercept of f(x) = -3}$

$\text{y-intercept of g(x) = -5}$

$-3 > -5$

f(x) has the greater y-intercept.