**Answer:**

**A. Both of Johny's (f(x)) and David's functions (g(x)) are linear.**

**B. (f(x) - 75) ∝ x and g(x) ∝ x**

** where x = no. of working hours,**

** f(x), g(x) = money saved**

**C. Equation for Johny is, **

** y = 75 + 10x **

**where, x = no. of hours Johny works**

** y = money saved by Johny.**

**D. Equation for David is, **

** y = 20x **

**where, x = no. of hours David works**

** y = money saved by David**

**E. David will buy the X-box earlier. it can be found by putting f(x) = g(x) = 200 in the two equations and from that comparing the two values of x.**

**Step-by-step explanation:**

Let the equation for Johny be,

y = mx + c

where c is the y intercept which is here 75 and m is the slope of the straight line which is here ,

m =

= 10 [since (125 ,5) and (75 ,0) are over the straight line]

So, Johny's equation is,

y = 10x + 75 = f(x) [say]-------------------------------------------------(1)

which is linear.

Now slopes of different straight lines connecting the points for David are all equal to 20 ,

[since,

=

=

=

=

= 20]

So, David's equation is also a straight line with y intercept 0 and slope 20.

So, David's equation is,

y = 20x = g(x) [say] --------------------------(2)

A. Now, from (1) and (2) both of Johny's and David's functions are linear.

B. From (1) (f(x) - 75) ∝ x and from (2) g(x) ∝ x

C. Equation for Johny is,

y = 75 + 10x

where, x = no. of hours Johny works

y = money saved by Johny.

D. Equation for David is,

y = 20x

where, x = no. of hours David works

y = money saved by David

E. Putting y = 200 in (1) we get,

125 = 10x

⇒12.5 , so, Johny will earn the money in 12.5 hours.

and, putting y = 200 in (2) we get, x = 10 so, David will earn the money in 10 hours. since, 10 < 12.5 so, David will be able to purchase the X-box first.