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Which statement about the slopes of the functions is true? A. The slopes of the functions are the same in both the graph and the table. B.There is not enough information given to determine the slopes of the functions. C.The slope of the function shown in the graph is greater than the slope of the function shown in the table.. D The slope of the function shown in the table is greater than the slope of the function shown in the graph.

Answer :

In order to compare the slopes for the lines we need to find the slope of the function given in the table using the formula:

[tex]m=\frac{y_2-y_1}{x_2-x_{1_{\square}}}[/tex][tex]\begin{gathered} m=\frac{-6-(-3)}{-4-0} \\ m=-\frac{3}{-4} \\ m=\frac{3}{4} \end{gathered}[/tex]

then selecting two points for the function graphed we apply the formula and find the slope

points: (0,1) & (3,2)

[tex]\begin{gathered} m=\frac{2-1}{3-0} \\ m=\frac{1}{3} \end{gathered}[/tex]

then we know that

[tex]\frac{1}{3}<\frac{3}{4}[/tex]

for that reason the slope for the function shown in the table is greater than the slope in the graph.

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