The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −3 0 0 1 3 g(x) g(x) = 7x + 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. ! 1

Note that a straight line has an equation of the form
y = m*x + b
where
m = the slope
b = the y-intercept

Part A
The function f(x) is given by the table
x       -1    0    1       
f(x)   -3    0    3
Because f(0) = 0, the y-intercept is zero.
The slope is
m = (3 - (-3))/(1 - (-1)) = 6/2 = 3
Therefore
f(x) = 3x

g(x) = 7x +2
It has a slope of 7, and y-intercept of 2.
A plot of the two functions is shown below.


The slope of f(x) is 3.
The slope of g(x) is 7.

Part B.
f(x) has a y-intercept of 0.
g(x) has a y-intercept of 2.

g(x) has the greater y-intercept.

40 because it’s just a little longer than 32 feet