alyssaaa445
Answered

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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

Sagot :

Say that:

[tex]\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 } \\ \\ [/tex]

If this is the case,

[tex]y=\frac { 6 }{ 5 } x[/tex]

Another way to solve the problem,

[tex]y\propto x\\ \\ \therefore \quad y=kx[/tex]

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

[tex]12=k\cdot 10\\ \\ k=\frac { 12 }{ 10 } =\frac { 6 }{ 5 } \\ \\ \therefore \quad y=\frac { 6 }{ 5 } x[/tex]
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