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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).

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

[tex]m= \frac {9-1} {2-0} \\m= \frac {8}{2}\\m1=4[/tex]

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 [tex]b_1=1[/tex] Determine the slope of the function g(x) we have [tex]g(x)=3x+1[/tex] This is the equation of the line in slope-intercept form [tex]y=mx+b[/tex] where m is the slope b is the y-intercept so in this problem, [tex]m_2=3[/tex] [tex]b_2=1[/tex] Now compare the y-intercepts and slopes [tex]b_1=b_2[/tex] and [tex]m_1>m_2[/tex]

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