Answer:
Missing co-ordinate for the ordered pair is [tex](7,2834)[/tex]
Y-intercept is [tex](0,4682)[/tex]
X-intercept is [tex](17.73,0)[/tex]
Step-by-step explanation:
The number of a certain company's video stores can be approximated by the linear equation
[tex]y= -264\ x+4682[/tex]
where [tex]y[/tex] is the number of stores and [tex]x[/tex] represents the number of years after 1990.
To find the missing co-ordinate for the ordered pair solution [tex](7,?)[/tex]
For the ordered pair, we are given the [tex]x[/tex] value which is =7 i.e 7 years after 1990. Thus we will plugin [tex]x=7[/tex] in the linear equation to get the [tex]y[/tex] value which is number of stores after 7 years from 1990.
[tex]y= -264\ (7)+4682[/tex]
[tex]y= -1848+4682[/tex]
[tex]y= 2834[/tex]
Thus the ordered pair is [tex](7,2834)[/tex]
To find y-intercept which is the point where the line touches the y-axis, we would plugin [tex]x=0[/tex] in the equation as the x-coordinate is 0 at y-axis.
[tex]y= -264\ (0)+4682[/tex]
[tex]y= 0+4682[/tex]
[tex]y=4682[/tex]
Thus y-intercept is at point [tex](0,4682)[/tex]
To find x-intercept which is the point where the line touches the x-axis, we would plugin [tex]y=0[/tex] in the equation as the y-coordinate is 0 at x-axis and thus for [tex]x[/tex]
[tex]0= -264\ x+4682[/tex]
Subtracting both sides by 4682.
[tex]0-4682= -264\ x+4682-4682[/tex]
[tex]-4682= -264\ x[/tex]
Dividing both sides by -264
[tex]\frac{-4682}{-264}= \frac{-264\ x}{-264}[/tex]
[tex]17.73= x[/tex]
∴ [tex]x=17.73[/tex]
Thus x-intercept is at point [tex](17.73,0)[/tex]
