Question

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

Answer 1

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

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

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

Answer 2

Answer:

Option C.

Step-by-step explanation:

The slope intercept form of a line is

$y=mx+b$        .... (1)

The given function is

$y=x+4$           ..... (2)

On comparing (1) and (2) we get

$m=1$

Rate of change of first function is 1.

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

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

$m=\dfrac{8-6}{2-0}$

$m=\dfrac{2}{2}$

$m=1$

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.