Question

Are the graphs of the equations parallel, perpendicular, or neither? y= 2x +6 and y= 1/2x +3

Answer 1

Given the equations:

`\begin{gathered} y=2x+6 \\ y=(1)/(2)x+3 \end{gathered}`

The equation has the form of slope - intercept form which is like:

`y=m\cdot x+b`

Where m is the slope and b is y- intercept

So,

The slope of the first equation = 2

The slope of the second equation = 1/2

The graphs of the equations are parallel when the slopes are equal

The graphs of the equations are perpendicular when the product of the slopes = -1

so,

the slopes are not equal

The product of the slopes = 2 * 1/2 = 1

So, the graphs of the equations are neither parallel nor perpendicular.