Question

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

x y

-38 40

-23 30

-8 20
find the x intercept

Answer 1

(22, 0)

Explanation:

Answer 2

The x-intercept is the point (22,0)

Explanation:

step 1

Find the slope

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

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

take the points

(-38,40) and (-23,30)

substitute the given values

`m=(30-40)/(-23+38)`

`m=(-10)/(15)`

`m=-(2)/(3)`

step 2

Find the equation of the line in point slope form

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

we have

`m=-(2)/(3)`

`point\ (-8,20)`

substitute

`y-20=-(2)/(3)(x+8)`

step 3

Find the x-intercept

Remember that the x-intercept is the value of x when the value of y is equal to zero

so

For y=0

`0-20=-(2)/(3)(x+8)`

solve for x

`-20=-(2)/(3)x-(16)/(3)`

Multiply by 3 both sides

`-60=-2x-16`

`2x=60-16\\2x=44\\x=22`

therefore

The x-intercept is the point (22,0)