Question

The number of a certain company's video stores can be approximated by the linear equation y= -264x+4682, where x is the number of years after 1990.

Find the missing coordinate for the ordered pair solution (7,?)

-What's the y-interpret and x-interpret?

Answer 1

Missing co-ordinate for the ordered pair is
`(7,2834)`

Y-intercept is
`(0,4682)`

X-intercept is
`(17.73,0)`

Explanation:

The number of a certain company's video stores can be approximated by the linear equation

`y= -264\ x+4682`

where
`y` is the number of stores and
`x` represents the number of years after 1990.

To find the missing co-ordinate for the ordered pair solution
`(7,?)`

For the ordered pair, we are given the
`x` value which is =7 i.e 7 years after 1990. Thus we will plugin
`x=7` in the linear equation to get the
`y` value which is number of stores after 7 years from 1990.

`y= -264\ (7)+4682`

`y= -1848+4682`

`y= 2834`

Thus the ordered pair is
`(7,2834)`

To find y-intercept which is the point where the line touches the y-axis, we would plugin
`x=0` in the equation as the x-coordinate is 0 at y-axis.

`y= -264\ (0)+4682`

`y= 0+4682`

`y=4682`

Thus y-intercept is at point
`(0,4682)`

To find x-intercept which is the point where the line touches the x-axis, we would plugin
`y=0` in the equation as the y-coordinate is 0 at x-axis and thus for
`x`

`0= -264\ x+4682`

Subtracting both sides by 4682.

`0-4682= -264\ x+4682-4682`

`-4682= -264\ x`

Dividing both sides by -264

`(-4682)/(-264)= (-264\ x)/(-264)`

`17.73= x`

∴
`x=17.73`

Thus x-intercept is at point
`(17.73,0)`