Answer:[tex]P=\frac{x}{16000}+6.5[/tex]
Step-by-step explanation:
Given
Spectator or attendance [tex](x)=56,000[/tex]
Price [tex]P=\$ 10[/tex]
When ticket price lowered by [tex]P=\$ 8[/tex]
attendance [tex](x)=24,000[/tex]
Suppose they follow a linear relation then
[tex]P=mx+C[/tex]
where [tex]C=constant[/tex]
for [tex]x=56,000[/tex]
[tex]10=56,000m+C\ldots (i)[/tex]
For [tex]x=24,000[/tex]
[tex]8=24,000+C\ldots (ii)[/tex]
From (i) and (ii) we get
[tex]2=32000m[/tex]
[tex]m=\frac{1}{16000}[/tex]
substitute the value of m to get [tex]C[/tex]
[tex]10=56,000\times \frac{1}{16000}+C[/tex]
[tex]C=6.5[/tex]
Therefore the required equation becomes
[tex]P=\frac{x}{16000}+6.5[/tex]
