Part a: explain why the x-coordinates of the points where the graphs of the equations y = 2x and y = 4x-2 intersect are the solutions of the equation 2x = 4x-2. (4 points)

part b: make tables to find the solution to 2x = 4x-2. take the integer values of x only between -1 and 3. (4 points)

part c: how can you solve the equation 2x = 4x-2 graphically?

Step-by-step explanation:

Part A: the x coordinates of the points where the graphs of those equations intersect is 2x = 4x - 2 because this is where the values for the function are the same for the two equations.

Part B: solving the equation:

2x = 4x -2

2x=2

x=1, at x = 1 the graphs intersect

---Tables to find the solution:

for x = - 1

2x = -2, 4x -2 = -6

for x = 0

2x = 0, 4x - 2 = -2

for x = 1

2x = 2, 4x -2 = 2

for x = 2

2x = 4, 4x -2 =6

for x = 3

2x =6, 4x -2 =10

We can see that for x = 1 both functions have the same value, so this  is the solution for 2x = 4x -2.

Part C: you can solve the equation 2x = 4x -2 by making the graphs for each function and indentifying the point where both lines intersect.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.