Question

The linear function graphed below represents Tim’s age in the years since he was married. Which of these statements is correct?

A graph titled Tim's Age During Marriage has years of marriage on the x-axis and Tim's Age on the y-axis. Points are at (22, 54), (37, 69), (52, 84).
The initial value is 22, and the rate of change is 1.
The initial value is 22, and the rate of change is 15.
The initial value is 32, and the rate of change is 1.
The initial value is 32, and the rate of change is 15

Answer 1

Required Answer:

The graph of the above data is not provided, but still we can predict the answer through the coordinates having specific meaning.

• Tim's Age During Marriage has years of marriage on the x-axis.
• Tim's Age on the y-axis.

The first coordinate is (22, 54). So the initial value of the data is 22, years of marriage. And rate of change can be found by:

$\sf{ \longrightarrow{ \dfrac{y2 - y1}{x2 - x1} }}$

Let's consider:

• (x1 , y1) be (22, 54)
• (x2 , y2) be (37, 69)

Plugging in the above formula,

$\sf{ \longrightarrow{ \dfrac{69 - 54}{37 - 25} }}$

$\sf{ \longrightarrow{ \dfrac{15}{15} = \boxed{\bf{1}}}}$

The rate of change of the years of marriage and Tim's Age is given by 1.

So, The correct answer is $\large{\underline{\boxed{\bf{\purple{Option \: A}}}}}$

And we are done !!

Answer 2

GIVEN :-

• The linear function graphed attachment above represents Tim’s age in the years since he was married .

1. In x-axis :- Year of marriage .
2. In y-axis :- Tim's age during marriage .

TO FIND :-

• The initial value and the rate of change from the above graph .

SOLUTION :-

☯︎ From the given graph, The starting point is (22 , 54) as shown .

• i.e. the initial value from the data is 22 .

➪ Now, we can find the rate of change . So firstly we can take any two points from the given graph .

[Note :- Take (either 1st point or 2nd point) or (either 2nd point or 3rd point) or (either 1st point or 3rd) .]

✯ The formula to find the rate of change is,

$\huge\red\star$ $\bf\purple{\dfrac{y_2\:-\:y_1}{x_2\:-\:x_1}}$

✵ Now, we take two points, i.e.

1. (22 , 54)
2. (37 , 69)

Where,

• $\bf\red{y_2}$ = 69

• $\bf\red{y_1}$ = 54

• $\bf\red{x_2}$ = 37

• $\bf\red{x_1}$ = 22

$\rm{:\implies\:Rate\:of\:change\:=\:\dfrac{69\:-\:54}{37\:-\:22}\:}$

$\rm{:\implies\:Rate\:of\:change\:=\:\dfrac{15}{15}\:}$

$\bf\green{:\implies\:Rate\:of\:change\:=\:1\:}$

$\huge\red\therefore$ [A] The initial value is "22" and the rate of change is "1" .