Question

On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 3, 0) and the y-axis at (0, 3). A straight blue line with a positive slope, labeled f of x, crosses the y-axis at (0, negative 3) and the x-axis at (1, 0). Both lines intersect at (3, 6). Which statement is true regarding the functions on the graph? f(6) = g(3) f(3) = g(3) f(3) = g(6) f(6) = g(6)

Answer 1

f(3)=g(3)

Explanation:

Edge 2021

Answer 2

f(3) = g(3)

Explanation:

we know that

When solve a system of linear equations by graphing, the solution of the system is the intersection point both lines

The intersection point is common point for bot lines

In this problem

we have the system of equations

f(x)

g(x)

The intersection point is (3,6)

That means that the solution for the system is the point (3,6)

so

For x=3

The value of f(3)=6 and the value of g(3)=3

therefore

f(3)=g(3)

Verify the statements

Find the equation of the blue line f(x)

(0,-3) and (1,0)

the slope is

`m=(0+3)/(1-0)=3`

The equation in slope intercept form is equal to

`f(x)=3x-3`

Find the equation of the red line g(x)

(-3,0) and (0,3)

the slope is

`m=(3-0)/(0+3)=1`

The equation in slope intercept form is equal to

`g(x)=x+3`

case 1) f(6) = g(3)

The statement is false

Because

For x=6 ----->
`f(6)=3(6)-3=15`

For x=3 ---->
`g(3)=3+3=6`

therefore

`f(6) \\eq g(3)`

case 2) f(3) = g(3)

The statement is true

Because

For x=3 ----->
`f(3)=3(3)-3=6`

For x=3 ---->
`g(3)=3+3=6`

therefore

`f(3)=g(3)`

case 3) f(3) = g(6)

The statement is false

Because

For x=3 ----->
`f(3)=3(3)-3=6`

For x=6 ---->
`g(6)=6+3=9`

therefore

`f(3) \\eq g(6)`

case 4) f(6) = g(6)

The statement is false

Because

For x=6 ----->
`f(6)=3(6)-3=15`

For x=6 ---->
`g(6)=6+3=9`

therefore

`f(6) \\eq g(6)`