Determine whether y varies directly with x if so, solve for the constant of variation k. 3y= -7x-18

Question:

Determine whether y varies directly with x if so, solve for the constant of variation k.

3y= -7x-18

Variation:

(i) If y varies directly as x then {eq}y=kx {/eq}, where 'k' is a constant of variation.

(ii) If y varies inversely as x then {eq}y= \dfrac{n}{x} {/eq}, where 'n' is a constant of variation.

Answer and Explanation:

The given equation is:

$$3y= -7x-18 $$

Dividing both sides by {eq}3 {/eq},

$$y= \dfrac{-7}{3}x - 6 \,\,\,\,\,\,\rightarrow (1) $$

If {eq}y {/eq} varies directly with {eq}x {/eq}, then the relation between them should be of the form {eq}y= kx {/eq}, where {eq}k {/eq} is a constant of variation.

But (1) is NOT of this form (as a constant is extra).

Therefore, {eq}y {/eq} does NOT vary directly with {eq}x {/eq}.


Learn more about this topic:

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Solving Equations of Direct Variation

from Algebra I: High School

Chapter 17 / Lesson 9
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