Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−2 intersect are the solutions of the equation 4x = 2x−2. (4 points) Part B: Make tables to find the solution to 4x = 2x−2. Take the integer values of x between −3 and 3. (4 points) Part C: How can you solve the equation 4x = 2x−2 graphically? (2 points) (10 points)

Answer 1

Answer with explanation:

The equation of two curves are

   y=4 x-----(1)

 y=2x-2-------(2)

To find the solution of the equations above , we need to find their point of Intersection.

To find the point of Intersection of these two curves equate y values of the above two equations.

So, 4 x=2x-2 , is the required equation to find the point of intersectin of two curves.

2.

         x=       -3        -2         -1         0       1          2            3

LHS=4 x       -12        -8         -4        0       4         8           12

RHS=2x-2     -8         -6          -4        -2      0         2           4

At, x= -1, the two , 4x and 2x-2 are equal.

3.

To solve the equation graphically

     4 x=2 x-2

Plot, y=4x , and , y=4 x-2 , in the coordinate plane.The point of intersection of these two curves will give x and y value.

     

Answer 2

Part A:
 We observe that we have the following system of equations:
 y = 4x
 y = 2x-2
 The solution to the system of equations is an ordered pair (x, y), that is, a point in common that both functions have.

 Part B:

 x    y = 4x    y = 2x-2
 -3     -12           -8
 -2      -8            -6
 -1      -4            -4
  0       0            -2
  1       4             0
  2       8             2
  3      12            4
 The solution is the ordered pair:
 (x, y) = (-1, -4)

 Part C:
 See attached image