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

Explanation:

A: The expression 4x = 2x - 2 reduces to x = -1. This is true for all values of y, since y is not a factor in this expression.

The two other equations intersect at point (-1, -4). See the attached graph (Solutions2)

y = 4x

y = 2x−2

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Mathematically, we can substitute the value of y from the first equation into the second:

y = 2x−2

(4x) = 2x−2

2x = -2

x = -1

The intersection of this two lines is (-1,-4). Since x=-1, this is also the solution to 4x=2x-2, as per the above.

B: See attached Result Table

C: See GraphEquation2