Part A:
To find the slope of f(x), use the following formula to find the slope:
[tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Choose any two points from the table. We'll use (-1, -6) and (1, 0):
[tex] \frac{0 - (-6)}{1 - (-1)} = \frac{6}{2} = 3 [/tex]
The slope of f(x) is 3.
g(x) uses slope intercept form, which uses the following formula:
[tex] y = mx + b [/tex]
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:
[tex] \text{slope of f(x) = 3} [/tex]
[tex] \text{slope of g(x) = 4} [/tex]
[tex] 3 < 4 [/tex]
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:
[tex] \text{y-intercept of f(x) = -3} [/tex]
[tex] \text{y-intercept of g(x) = -5} [/tex]
[tex] -3 > -5 [/tex]
f(x) has the greater y-intercept.
