Answer:
[tex]y = 7.5[/tex]
Step-by-step explanation:
Given
Direct variation implies that:
[tex]y = kx[/tex]
Where k is the constant of variation.
[tex]x=4; y=3[/tex]
Required
Find y when [tex]x = 10[/tex]
[tex]y = kx[/tex]
Make k the subject
[tex]k = \frac{y}{x}[/tex]
For: [tex]x=4; y=3[/tex]
[tex]k = \frac{3}{4}[/tex]
For: [tex]x = 10[/tex]
[tex]k = \frac{y}{x}[/tex] becomes
[tex]k = \frac{y}{10}[/tex]
Substitute [tex]k = \frac{3}{4}[/tex]
[tex]\frac{3}{4} = \frac{y}{10}[/tex]
Make y the subject
[tex]y = \frac{3}{4} * 10[/tex]
[tex]y = \frac{3* 10}{4}[/tex]
[tex]y = \frac{30}{4}[/tex]
[tex]y = 7.5[/tex]
