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contestada

The rate of change in the function y=x+4 is________ the rate of change of the function represented in the table.

A) greater than

B) less than

C) equal to

x/y
0/6
2/8
4/10
6/12

Respuesta :

recall that the slope is the "average rate of change" of any function.

[tex]\bf y=\stackrel{slope}{1}x+4\qquad \qquad \begin{array}{ccll} x&y\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 0&6\\2&8\\4&10\\6&12 \end{array} \\\\\\ \textit{let's check what is the slope of the tabled function}\\ \textit{by using two points from it}[/tex]

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ 8}})\quad % (c,d) &({{ 6}}\quad ,&{{ 12}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{12-8}{6-2}\implies \cfrac{4}{4}\implies 1[/tex]

Answer:

Option C.

Step-by-step explanation:

The slope intercept form of a line is

[tex]y=mx+b[/tex]        .... (1)

The given function is

[tex]y=x+4[/tex]           ..... (2)

On comparing (1) and (2) we get

[tex]m=1[/tex]

Rate of change of first function is 1.

If a line passes through two points [tex](x_1,y_1), and (x_2,y_2)[/tex], the rate of change of the line is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the given table it is clear that the line passes through two points (0,6) and (2,8). So, the rate of change of second function is

[tex]m=\dfrac{8-6}{2-0}[/tex]

[tex]m=\dfrac{2}{2}[/tex]

[tex]m=1[/tex]

Rate of change of second function is 1.

The rate of change in the function y=x+4 is equal to the rate of change of the function represented in the table.

Therefore, the correct option is C.

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