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)

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: .75 km

step-by-step explanation:

b

step-by-step explanation: