A: Looking at the last two rows of the table of f(x), the slope is simply (3-0)/(1-0) = 3, while the slope of g(x) is the coefficient of the variable x, which is 7.
B. y-int is the y value when x = 0. f(x) has a y-int of 0, which g(x) is 2. The latter has a greater y-int.
Answer:
Part A: The slope of g(x) is greater than the slope of f(x).
Part B: Function g(x) has greater y-intercept.
Step-by-step explanation:
The function f(x) passes through the points (-1,-3), (0,0) and (1,3). It means the y-intercept of the function is 0.
If a line passes through two points, then the slope of the function is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let as consider any two points of the function, (-1,-3) and (0,0).
[tex]m=\frac{0+3}{0+1}=3[/tex]
The point slope form of a linear function is
[tex]m=mx+b[/tex] .... (1)
Where, m is slope and b is y-intercept.
The slope of f(x) is 3 and y-intercept is 0, therefore the function f(x) is
[tex]f(x)=3x[/tex]
The given function is
[tex]g(x)=7x+2[/tex] .... (2)
From (1) and (2), we get
[tex]m=7,b=2[/tex]
The slope of g(x) is 3 and y-intercept is 2.
Part A: Since the slope of f(x) is 3 and the slope of g(x) is 7, therefore the slope of g(x) is greater than the slope of f(x).
Part B: Since the y-intercept of f(x) is 0 and y-intercept of g(x) is 2, therefore the function g(x) has greater y-intercept.
