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?
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.