Calculating for X or Y in a pattern

Question

X: 3 6 9 12 15

Y: 2 4 6 8 10

Find the Rule for Y

Answer 1

Looks like every time x goes up by 3, y goes up by 2. There is a constant rate of change so the rule for y is linear. Think slope is rise over run where run is the change in x. Try 2 over 3 or m = 2/3. Or, once you know the relationship is linear use the formula for slope between any two points: m = (4 - 2) / (6 - 3) = 2/3.

Now the question is what is the y-intercept? Use point-slope or slope-intercept.

Point-Slope:

y - 2 = (2/3)(x - 3)

y - 2 = (2/3)x - 2

y = (2/3)x

Slope-Intercept:

y = mx + b

2 = (2/3)3 + b

2 = 2+b

b = 0

y = (2/3) x

desmos.com/calculator/5ucc4k02cs

Answer 2

The Rule of y in a series such as the one you have is simply how does y change as x changes.

GIVEN:

X: 3 6 9 12 15

Y: 2 4 6 8 10

We can see that x increases by 3 every time and that y increases by 2 every time.

So very simply put the Rule of y is that y increases by 2 when x increases by 3.

Good luck on your exams!

Answer 3

If we're strictly looking at the pattern of y, it follows an arithmetic sequence where each successive y term increases by 2. If we're looking at predicting the y value as a function of x, then we can calculate the rate of change( slope) and note that delta y = 2, and delta x =3, hence, y is 2/3 of whatever x value is entered.

Since the original statement mentions calculating for x OR y, we can use the sequential logic if we needed to find the next x or y term. Since the function is linear (has a constant rate of change), if you were asked to predict the next x value, for example, we can see that each x term increases by 3 from the previous term. You could either write it as delta x is equal to 3 or :

x(n) = x(n-1)+3 ## where n represents the term you're on and '+3' represents the change in x

For example, if you want to calculate x(6)--the sixth x term, it would be equal to:

x(6) = x(6-1)+3

x(6) = x(5) +3 --> x(5) = 15

x(6) = 15+3

x(6) = 18

We could do the exact same for y:

y(n) = y(n-1)+2 ## where n represents the term you're on and '+2' represents the change in y

y(6) = y(6-1) +2

y(6) = y(5) +2

y(6) = 10 + 2

y(6) = 12

Calculating the 6th term was pretty easy considering the sequence stopped on the 5th term (you could easily eye it), but imagine if someone asked for the 20th term; having a formula is pretty handy in either case.

Hope this helps!

Answer 4

Hi Sarah,

By itself, y increases by 2.

To find it in relation to x, it consistently can be divided by 1.5.

Answer 5

y =2x/3

as each y value is 2/3 of its corresponding x value

x=3y/2 as each x value is 1.5 or 3/2 times its corresponding y value