Hey there mate :)
As per question,
Options (a), (b) and (d) are correct.
<h3>Proof :-</h3>
(a) <em><u>The cost per visit to a community pool.</u></em>
Considering x = number of visits to the pool
a = fixed cost of visit.
So, the cost per visit to the pool y will be ax
Therefore, this represents a linear function.
And
<em><u>The neighborhood charges a yearly fee to use the pool.</u></em>
Assuming x = number of years
a = fixed fee to use the pool
So the yearly fee to use the pool y will be ax
Therefore, this represents a linear function.
(b) <em><u>The cost to attend a show at the local theater. Tickets are $12 each.</u></em>
Let x = number of shows
Let the cost of one show = $12.
Now, the cost of x shows y will be 12x
So, it represents a linear function.
(d) <em><u>The distance a bicyclist travels when cycling at a constant speed of 30 mph. </u></em>
Assuming <em>x</em>= time
Speed = 30 mph.
Since the distance (y) is given as:-
Distance = Speed×time, so,
<em>=> y = 30x</em>
Hence, this also represents a linear function.
<u>Hence, all correct option are proved</u>