Question

This table gives a few (x, y) pairs of a line in the coordinate plane.

x y
22 36
27 54
32 72

What is the x-intercept of the line?

Answer 1

(12,0)

Explanation:

Let us find the equation of the line with the help of two point form of a line

Here take any two coordinates

say (22,36) and (27,54)

The two point form says

`(y-y_(1))/(x-x_(1))=(y_(2)-y_(1))/(x_(2)-x_(1))`

Putting the values in above formula

`(y-36)/(x-22)=(54-36)/(27-22)`

`(y-36)/(x-22)=(18)/(5)`

`y-36=(18)/(5) * (x-22)`

`y=(18)/(5) * (x-22) + 36`

In order to determine the x intercept we put y = 0 and solve it for x

`0-36=(18)/(5) * (x-22)`

`-36 * (5)/(18)=(x-22)`

`-10=x-22`

adding 22 on both sides we get

x=12

Hence the x intercept is 12