Question

The line with equation y = 2x + 3 is reflected in the x-axis.
Which of the following is the equation of the new line?
y=2x-3, Y=-2x+3, x=2y+3, y=-2x-3

Answer 1

Answer:

Answer by Theo(11143) (Show Source): You can put this solution on YOUR website!

when the equation is reflected about the y-axis.

(x,y) becomes (-x,y)

you get the same y value that is the same distance from the y-axis but on opposite sides of it.

in f(x) terms, this means that f(x) is equal to f(-x)

your original equation is y = 2x + 3

replace x with (-x) an dyou get y = 2 * -x + 3 which becomes y = -2x + 3.

that's your reflected equation.

the graph of both equations will show you that the equations are symmetric about the y-axis.

this means that x = 3 becomes y = 2x + 3 which becomes y = 9 in the original equation.

this means that x = -3 becomes y = -2x + 3 which becomes y = 9 in the reflected equation.

the graphs looks like this:

a horizontal line has been placed at y = 9 so you can see that, when y = 9, x = 3 or -3.

Answer 2

Final Answer:

The equation of the new line that is formed when the line with the equation $y = 2x + 3$  is reflected in the x-axis, is $y = -2x- 3$. The corresponding correct option is the fourth option.

Given:

The line with the equation $y = 2x + 3$ is reflected in the x-axis.

To Find:

The equation of the new line and the corresponding correct option among $y=2x-3, Y=-2x+3, x=2y+3, y=-2x-3$.

Explanation:

In a graph, any point (x,y) on being reflected in the x-axis will change to the reflected point (x,−y).

• it implies that the x-value of the new coordinate remains the same and need not change its sign.

• Only, the y-value of the new coordinate is required to change its sign from positive to negative or vice-versa (as applicable).

Step 1 of 3

Here, the line with the equation $y = 2x + 3$ is reflected in the x-axis. So the x-value of the newly reflected coordinate remains the same.

Step 2 of 3

The y-value of the newly reflected coordinate remains in the same magnitude but changes from y to -y in its equation.

Step 3 of 3

The line with the equation $y = 2x + 3$ is reflected in the x-axis is shown with the following equation.

$-y = 2x + 3\\y = -2x- 3$

Therefore, the equation of the new line that is formed when the line with the equation $y = 2x + 3$  is reflected in the x-axis, is $y = -2x- 3$. The corresponding correct option is the fourth option.

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