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

The x-intercept of the line is the point (12,0)

Explanation:

step 1

Find the slope of the lime

Take the points

(22,36) and (32,72)

The formula to calculate the slope between two points is equal to

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

substitute the values

`m=(72-36)/(32-22)`

`m=(36)/(10)`

`m=3.6`

step 2

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

we have

`m=3.6`

`point (22,36)`

substitute

`y-36=3.6(x-22)`

step 3

Find the x-intercept

we know that

The x-intercept of a line is the value of x when the value of y is equal to zero

so

For y=0

substitute in the equation and solve for x

`0-36=3.6(x-22)`

`0-36=3.6x-79.2`

`3.6x=79.2-36`

`3.6x=43.2`

`x=12`

therefore

The x-intercept of the line is the point (12,0)