Question

ANSWER ASAPP please i really need help

Answer 1

Part a:

Line A:
`y=(2)/(3) x`

Line B:
`y=(1)/(3) x+2`

Part b:

solution: (6,4)

Part c:

`4=(2)/(3) (6)\\4=(12)/(3) \\4=4`

`4=(1)/(3) (6)+2\\4=(6)/(3) +2\\4=2+2\\4=4`

Part d:

(3,2): A

(4,6): neither

(3,3): B

(6,4): Both

Explanation:

The slope intercept form is y=mx+b

m=slope

b= y intercept

To find The equation for line A we first find the slope by doing the slope formula

`(y_(2)-y_(1) )/(x_(2)-x_(1)) \\`

I will use the points (3,2) and (6,4)

`(4-2)/(6-3)`

`(2)/(3)`

And we can see the y intercept is at 0 so we can fill in this information

`y=(2)/(3) x`

Now for line B to find the slope I will use points (3,3) and (6,4)

`(4-3)/(6-3) \\(1)/(3)`

We know the y intercept is 2 because of where the line intersects with the y axis

`y=(1)/(3) x+2`

Part B:

The solution to the system of equations are where the lines intersect and that happens at (6,4)

Part C:

To prove it we just fill in the the coordinates into the equation as shown above

Part D:

We just see which line these points are on

(3,2) is on line A

(4,6) is on neither line

(3,3) Is on line B

(6,4) is on both lines (hence it was the solution to the system of equations)

Hope this helps pleas let me know if you have further questions