Question

Lucy is knitting a blanket and needs to buy some more yarn. At her local craft store, 2 skeins of yarn cost $7 and 8 Skeins of yarn cost $28. Which equation represents this direct variation

Answer 1

Answer:

$y = 3.5x$

Where y is the cost and x is the number of skeins of yarn.

Step-by-step explanation:

To model this situation we can use the linear equation:

$y = ax + b$

Where y is the cost, x is the number of skeins of yarn, a is the slope of the equation and b is the y-intercept.

If 2 skeins of yarn cost $7, we have that:

$7 = 2a + b$

If 8 skeins of yarn cost $28, we have that:

$28 = 8a + b$

Multiplying the first equation by 4 and subtracting the second equation from it, we have:

$4*7 - 28 = 4*(2a + b) - 8a - b$

$28-28 = 8a + 4b - 8a - b$

$0 = 3b$

$b = 0$

Now, finding the value of a, we have:

$7 = 2a + b$

$7 = 2a + 0$

$a = 3.5$

So our equation is:

$y = 3.5x$