Question

For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation

x y
10 12
15 18
20 24

Answer 1

y=1.2x

Explanation:

Answer 2

Say that:


`\left( { x }_( 1 ),{ y }_( 1 ) \right) =\left( 10,12 \right) \\ \\ \left( { x }_( 2 ),{ y }_( 2 ) \right) =\left( 15,18 \right) \\ \\ \therefore \quad \frac { \delta y }{ \delta x } =\frac { { y }_( 2 )-{ y }_( 1 ) }{ { x }_( 2 )-{ x }_( 1 ) } =\frac { 18-12 }{ 15-10 } =\frac { 6 }{ 5 } \\ \\`

If this is the case,


`y=\frac { 6 }{ 5 } x`

Another way to solve the problem,


`y\propto x\\ \\ \therefore \quad y=kx`

When x=10, y=12, so...


`12=k\cdot 10\\ \\ k=\frac { 12 }{ 10 } =\frac { 6 }{ 5 } \\ \\ \therefore \quad y=\frac { 6 }{ 5 } x`