Answer:
The slope of f(x) is equal to the slope of g(x).
Step-by-step explanation:
First, you need to calculate the slope of f(x) and g(x) using the slope formula
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are points of the functions.
To calculate the slope of f(x) you can choose two points from the graph, in this case (0, -1) and (3, 1).
m = 1 - (-1) / 3 - 0
m = 1 + 1 / 3
m = 2 / 3
m = 0.66...
To calculate the slope of g(x) you can choose two points from the table, in this case (0, 2) and (3, 4).
m = 4 - 2 / 3 - 0
m = 2 / 3
m = 0.66...
So the slope of f(x) is equal to the slope of g(x).
Slope of a linear function passing through two points [tex](h, k)[/tex] and [tex](a,b)[/tex] is defined by the expression,
Slope = [tex]\frac{k-b}{h-a}[/tex]
Slope of both the functions 'f' and 'g' are equal. Option (3) will be the answer.
Slope of function 'f' passing through two points (0, -1) and (3, 1) will be,
Slope of function 'f' = [tex]\frac{-1-1}{0-3}[/tex]
= [tex]\frac{2}{3}[/tex]
Similarly, from the table attached,
Slope of the function 'g' passing through (0, 2) and (3, 4) will be,
Slope of function 'g' = [tex]\frac{2-4}{0-3}[/tex]
= [tex]\frac{2}{3}[/tex]
Therefore, slope of function 'g' and slope of function 'f' are same.
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