Direct Variation Question 1 with Solutions

Direct Variation Question 1 with Solutions

Yesterday, I went over direct variation, and I gave you three direct variation problems to try on your own. You can see that post here: Direct Variation

Today I would like to give a solution to the first of those three problems. I will give solutions to the other two problems throughout this week.

**Example: **If *y* = *kx* and *y* = 7 when *x* = 11, then what is *y* when *x* = 33?

Try to solve the problem yourself before checking the solutions below.

**Solutions: **

**(1) **We are given that *y* = 7 when *x* = 11, so that 7 = *k*(11), or *k* = 7/11. Therefore *y* = 7*x*/11. When *x* = 33, we have *y* = 7(33)/11 = **21**.

**(2) **Since *y* varies directly as *x*, *y*/*x *is a constant. So, we get the following ratio: 7/11 = *y*/33. Cross multiplying gives 231 = 11*y*, so that *y* = **21**.

**(3) **The graph of *y* = *f*(*x*) is a line passing through the points (0,0) and (11, 7) The slope of this line is (7 – 0)/(11 – 0) = 7/11. Writing the equation of the line in slope-intercept form we have *y* = 7/11 *x*. As in solution 1, when *x* = 33, we have *y* = 7(33)/11 = **21**.

**(4) **To get from *x* = 11 to *x* = 33 we multiply *x* by 3. So we have to also multiply *y* by 3. We get 3(7) = **21**.

**More Problems with Explanations**

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