How to find missing number.,(180,14) (120,8) (?,4) (220,18)

Answer 1

42

Answer 2

Write these pairs from largest to smallest.

120 , 8

180 , 14

220 , 18

Assume these are the coordinates of a straight line with gradient m.

For the first and secong pair differences betwen coordinates are:

x2 - x1 = 180 - 120 = 60

y2 - y1 = 14 - 8 = 6

m = ( y2 - y1 ) / ( x2 - x1 ) = 6 / 60 = 1 / 10

For the third and fourth pair differences betwen coordinates are:
x3 - x2 = 220 - 180 = 40

y3 - y2 = 18 - 14 = 4

m = ( y3 - y2 ) / ( x3 - x2 ) = 4 / 40 = 1 / 10

You can see, for both pairs the gradients are the same and it is a straigth line with a gradient:

m = 1 /10

Vrite equation of straigth line in slooe-intecept form.

y = m x + b

In this case:

y = 1 / 10 x + b

Take any pair of points, for example the first to calculate b.

x = 120 , y = 8

y = 1 / 10 x + b

8 = 1 / 10 • 120 + b

8 = 12 + b

Subtract 12 to both sides

8 - 12 = b

- 4 = b

b = - 4

Equation of line is:

y = 1 / 10 x - 4

For missin pair y = 4

y = 1 / 10 x - 4

4 = 1 / 10 x - 4

Add 4 to bith sides.

8 = 1 / 10 x

Multiply both sides by 10

80 = x

x = 80

So missing number is 80