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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 between −4 and 4. (4 points)

Part C: How can you solve the equation 2x = 4x−2 graphically? (2 points)

Respuesta :

MrsStrong

Answer:

See below.

Step-by-step explanation:

Part A: You can solve the equations for an x value which make both true. You do this by setting each equation equal and using inverse operations.

2x = 4x - 2

2x - 4x = 4x - 4x - 2

-2x = -2

x = 1

Part B: You can make a table by substituting the values -4 to 4 in each equation and simplifying.

x     y = 2x      y = 4x - 2

-4           -8            -18

-3           -6             -14

-2           -4             -10

-1             -2            -6

0              0             -2

1               2              2

2              4              6

3              6              10

4              8              14

Part C: You can graph each equation and where they intersect will be the solution. They intersect at (1, 2). This is where they have the exact same x and y value in the table as well.

david8644

Answer:

When X= 1 both graphs are in (1,2)

Step-by-step explanation:

In order to evaluate the first part, where the lines intersect is you just have to equalize in opposite sides of the equation both equations:

2x=4x-2

Then you have to clear the x

2x-4x=-2

-2x=-2

x=[tex]\frac{-2}{-2}[/tex]

x=1

So your coordinates are x=1, and the Y coordinate you just evaluate one of the equations:

y=4x-2

y=4(1)-2

y=4-2

y=2

So your coordinate for y=2.

Part B, table.

To evaluate this, you just make a table, giving values to x, and you evaluate the Y:

X----Y

-4    -8

-3    -6

-2    -4

-1     -2

0      0

1       1

2      4

3     6

4     8

Part C.

YOu just hava to put it into the graph by evaluating with the tables above.

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