Question

Determine the intercepts of the line that correspond to the following table of values.

Answer 1

Part 1) The x-intercept is the point (-5,0)

Par 2) The y-intercept is the point (0,-17.5)

Explanation:

step 1

Find the x-intercept

we know that

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

Observing the table

For x=-5, y=0

therefore

The x-intercept is the point (-5,0)

step 2

Find the equation of the line

Find the slope m

we have

(-7,7) and (-5,0)

`m=(0-7)/(-5+7)\\ m=-3.5`

Find the equation of the line into point slope form

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

we have

`m=-3.5`

point (-5,0)

substitute

`y-0=-3.5(x+5)`

`y=-3.5(x+5)`

Find the y-intercept

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

For x=0

`y=-3.5(0+5)`

`y=-17.5`

therefore

The y-intercept is the point (0,-17.5)