Question

Table of values of a linear function is shown below. Find the output when the input is n. Type your answer in the space provided.

input 1 2 3 4 n
output 10 13 16 19

Answer 1

y = 3n + 7

Step-by-step explanation

n | y

---------

1 | 10

2 | 13

3 | 16

4 | 19

slope - (1, 10) ; (2, 13)

m = y1 - y2

-------------

n1 - n2

m = 10 - 13

-----------

1 - 2

m = 3

Slope Intercept Form Equation -

y - y1 = m(n - x1)

y - 10 = 3(n - 1)

y - 10 = 3n - 3

y = 3n - 7

Answer 2

y = 3n + 7

Explanation:

We can calculate a slope for the line defined by these points. (We are told it is linear, so we can use y = mx + b format, where m is the slope and b the y-intercept.)

Slope: I'll pick points (1,10) and (4,19) for calculating the slope:

Rise = (19-10) = 9

Run = (4-1) = 3

Rise/Run, or slope, m = (9/3, or 3

The equation becomes y = 3x + b

We can calculate b by using one of the given points. I'll pick (1,10):

y = 3x + b

10 = 3*(1) + b

b = 7

The equation is y = 3x + 7 It works for the other points (try it).

We can use n for x:

y = 3n + 7

Pick any n, and you'll have the correct outcome.