If the graph of a line x-2y=-1 in the xy-plane is relftected across the x-axis, what is the result equation of the reflection?

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lemjay | High School Teacher | (Level 3) Senior Educator

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When a line is reflected across the x-axis, its y-coordinates are all multiplied by -1. Thus, changing the sign of the values of y while the corresponding x-coordinates remain the same.

To determine the equation of a line when reflected across the x-axis, multiply the variable y by a negative.

 `x-2y = -1`

`x-2(-y) = -1`

 `x+2y = -1 `

x+2y=-1 is the reflection of x-2y=-1 across the x-axis.

To check, plot the two equations. Graph of x-2y=-1 is the red line. And x+2y=-1 is the blue one.

Base on the graph, the blue line is a reflection of the red line across the x-axis. Also, take note that for each values of x, the y-coordinates of the blue line are opposite in sign with the y-coordinates of the red line.

Hence, when x-2y=-1 is reflected across the x-axis, the resulting equation is x+2y=-1.