# Find the value of y for a given value of x, if y varies directly with x. If y = 39 when x = -117,...

## Question:

Find the value of {eq}y {/eq} for a given value of {eq}x {/eq}, if {eq}y {/eq} varies directly with {eq}x {/eq}.

If {eq}y = 39 {/eq} when {eq}x = -117 {/eq}, what is {eq}y {/eq} when {eq}x = -132 {/eq}?

## Direct Variation:

Direct variation explains the relationship between two variables which vary in the same direction. For variables that vary in the same direction, an increase/decrease in one variable causes an increase/decrease in the other variable.

If {eq}y {/eq} varies directly with {eq}x {/eq}, we can write this as:

• {eq}y \propto x {/eq}

Removing the proportionality sign and adding a constant:

• {eq}y = kx {/eq}

Given that {eq}y = 39 {/eq} when {eq}x = -117 {/eq}, the proportionality constant is equal to:

• {eq}39 = k(-117) {/eq}
• {eq}k = -\dfrac{39}{117} {/eq}

Therefore, the equation that gives the value of y for any given value of x is equal to:

• {eq}y = -\dfrac{39}{117} x {/eq}

Using the above equation, the value of y when x = -132 is equal to:

• {eq}y = -\dfrac{39}{117} (-132) {/eq}
• {eq}y = -\dfrac{39}{117} (-132) = \boxed{44} {/eq}