what is the missing value

Question

x | 1, 2, 3, 4, 5

y | 6,11,16,21,?

Answer 1

Hi

Given the values presented...these are clearly ordered points for the graph of a line.

Remember the slope-intercept form of a line, y = mx + b

Determine the slope, m which is the change in y over the change in x. It does not matter which two points you use, the slope will be the same.

m = (y2 - y1) /(x2 - x1)

I will use p1 = (1, 6) and p2 (2, 11)

m = (11-6)/(2-1) = 5/1 or 5

With m = 5, then the relationship between y and x is y = 5x + b

Need to find the value of b.

Notice that all the values of y are actually ONE more than 5 times x,

The final equation is y = 5x + 1

Check equation with the other values

Hope this helps :)

Answer 2

Hello, Alicia,

It helps to make a table and look for a pattern in the series. I'll use x to denote the series of integers (1,2,3, et.), and y as the value (6, 11, 16, etc.) assigned to each number in the series.

If we look at the difference (DIF) between each set of numbers as we go down the table, we see that each time x goes up by 1, y goes up by 5. That works until we get to the 5th in the series, since we aren't given a value, but are asked to supply it, instead.

If we add 5 to 21, we'll get 26. So it seems that the missing number is 26.

We could provide an equation for finding any number in the sequence: y = 5x + 1

Bob