Answer:
[tex]y=1.25x+3.5[/tex]
Step-by-step explanation:
Given:
The relation between the number of tickets and total cost for purchasing them.
Let [tex]y[/tex] represent number of tickets and [tex]x[/tex] represent the total cost to purchase them.
Now, let the relation be given by the following function:
[tex]y=mx+b[/tex], where, [tex]m[/tex] and [tex]b[/tex] are constants.
Let us find [tex]m[/tex] and [tex]b[/tex] using the values from the table.
For, [tex]x=7,y=12.25[/tex]. So,
[tex]12.25=7m+b\\or\ 7m+b=12.25------------1[/tex]
For, [tex]x=10,y=16[/tex]. So,
[tex]16=10m+b\\or\ 10m+b=16------------2[/tex]
Subtract equation 1 from equation 2. This gives,
[tex]10m+b-7m-b=16-12.25\\(10m-7m)+(b-b)=3.75\\3m=3.75\\m=\frac{3.75}{3}=1.25[/tex]
Now, plug in [tex]m=1.25[/tex] in equation 1 and solve for [tex]b[/tex].
[tex]7(1.25)+b=12.25\\8.75+b=12.25\\b=12.25-8.75=3.5[/tex]
Therefore, the function to represent the relationship between the tickets and total cost is given as:
[tex]y=mx+b\\y=1.25x+3.5[/tex]
