Question

Write an expression for the sequence shown below.

X Y
3 10
4 13
5 16
6 19
7 22

Answer 1

y changes by 3 when x changes by 1. So, the slope is 3
y = 3x+b
Now just plug in any pair of values to find b.

Answer 2

( 3, 10 ) , ( 4 , 13 ) , ( 5 , 16 ) , ( 6 , 19 ) , ( 7, 22 )

Change of x:

4 - 3 = 1

5 - 4 = 1

6 - 5 = 1

7 - 6 = 1

Change of y:

13 - 10 = 3

16 - 13 = 3

19 - 16 = 3

22 - 19 = 3

When x change for ∆x = 1 y is change for ∆y = 3

Slope m = ∆y / ∆x = 3 / 1 = 3

The "point-slope" form of the equation of a straight line is:

y − y1 = m ( x − x1 )

Take any point., for example ( 3, 10 ) which means x1 = 3 , y1 = 10

y − 10 = 3 ( x − 3 )

y - 10 = 3 ∙ x - 3 ∙ 3

y - 10 = 3 x - 9

Add 10 to both sides

y - 10 + 10 = 3 x - 9 + 10

y = 3 x + 1