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Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−1 intersect are the solutions of the equation 4x = 2x−1. (4 points)

Part B: Make tables to find the solution to 4x = 2x−1. Take the integer values of x between −4 and 4. (4 points)

Part C: How can you solve the equation 4x = 2x−1 graphically? (2 points)

(10 points)

Respuesta :

Answer:

Step-by-step explanation:

Part A

The reason why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−1 intersect are the solutions of the equation 4x = 2x−1 is because x is the independent variable. So the the value of y depends on the value of x and the value of x can only be found on the x axis. y can be determined by substituting the x coordinate into the given equation.

Part B

The equations of the two straight lines are y = 4x and y = 2x - 1. The table would be

For y = 4x

For x = - 4, y = - 16

For x = - 3, y = - 12

For x = -2, y = - 8

For x = -1, y = - 4

For x = 0, y = 0

For x = 1, y = 4

For x = 2, y = 8

For x = 3, y = 12

For x = 4, y = 16

For y = 2x - 1

For x = - 4, y = - 9

For x = -3, y = - 7

For x = -2, y = - 5

For x = -1, y = - 3

For x = 0, y = - 1

For x = 1, y = 1

For x = 2, y = 3

For x = 3, y = 5

For x = 4, y = 7

Part C

To solve graphically, select a suitable scale for the x and y axis of the graph.

For y = 4x, choose a scale of 1 cm to 1 unit on the x axis and 1 cm to 2 units on the y axis. Then plot the values of y on the y axis and the values of x on the x axis.

For y = 2x - 1, choose a scale of 1 cm to 1 unit on the x axis and 1 cm to 1 unit on the y axis. Then plot the values of y on the y axis and the values of x on the x axis.

Answer:

^In other words

Step-by-step explanation:

The reason why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−1 intersect are the solutions of the equation 4x = 2x−1 is that x is the independent variable. So the value of y depends on the value of x and the value of x can only be found on the x-axis. y can be determined by substituting the x coordinate into the given equation.  = - 4, y = - 9 For x = -3, y = - 7 For x = -2, y = - 5 For x = -1, y = - 3 For x = 0, y = - 1 For x = 1, y = 1 For x = 2, y = 3 For x = 3, y = 5 For x = 4, y = 7 To sFor y = 4x For x = - 4, y = - 16 For x = - 3, y = - 12 For x = -2, y = - 8 For x = -1, y = - 4 For x = 0, y = 0 For x = 1, y = 4 For x = 2, y = 8 For x = 3, y = 12 For x = 4, y = 16 For y = 2x - 1 For x olve graphically, select a suitable scale for the x and y-axis of the graph. For y = 4x, choose a scale of 1 cm to 1 unit on the x-axis and 1 cm to 2 units on the y-axis. Then plot the values of y on the y-axis and the values of x on the x-axis. For y = 2x - 1, choose a scale of 1 cm to 1 unit on the x-axis and 1 cm to 1 unit on the y-axis. Then plot the values of y on the y-axis and the values of x on the x-axis.

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