Question

Fill in each blank with the value for the system below:

Answer 1

Part a) The y-intercept of the linear function is the point
`(0,9)`

Part b) The y-intercept of the exponential function is the point
`(0,1)`

Part c) One point of intersection

Part d) The x-coordinate of the solution is
`1`

Part e) The y-coordinate of the solution is
`7`

Explanation:

we have

`y=2(4^(x))-1` -------> equation A

`y=-2x+9` ------> equation B

Part a) we know that

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

so

For
`x=0`

`y=-2(0)+9=9`

The y-intercept is the point
`(0,9)`

Part b) Find the y-intercept of the exponential function

For
`x=0`

`y=2(4^(0))-1=1`

The y-intercept is the point
`(0,1)`

Part c) The number of points of intersection

using a graphing tool

see the attached figure

One point of intersection

Part d) The x-coordinate of the solution

we know that

The solution of the system of equations is the intersection point both graphs

The intersection point is
`(1,7)`

therefore

The x-coordinate of the solution is
`1`

Part e) The y-coordinate of the solution

we know that

The solution of the system of equations is the intersection point both graphs

The intersection point is
`(1,7)`

therefore

The y-coordinate of the solution is
`7`