Question

PLEASE HELP THIS MEEDS TO BE RIGHT ITS DUE IN 5 MINUTES! I GIVE 30 POINTS!!!!

Compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
x f(x)
0 1
24
47
9(x) = 2x + 1
The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).

Answer 1

C.) The y-intercepts of both functions are the same and the function f(x) has a greater slope than the function g(x)

Explanation:

we know that the formula to calculate the slope between two points is equal to
`m= \frac {y1-y2}{x1-x2}` Determine the slope of the function f(x) take two points from the table (0,1) and (2,9) substitute in the formula

`m= \frac {9-1} {2-0} \\m= \frac {8}{2}\\m1=4`

Remember that the y-intercept is the value of y when the value of x is equal to zero in this problem, the point (0,1) is the y-intercept so
`b_1=1` Determine the slope of the function g(x) we have
`g(x)=3x+1` This is the equation of the line in slope-intercept form
`y=mx+b` where m is the slope b is the y-intercept so in this problem,
`m_2=3`
`b_2=1` Now compare the y-intercepts and slopes
`b_1=b_2` and
`m_1>m_2`

The y-intercepts of both functions are the same and the function f(x) has a greater slope than the function g(x)