Question

Which best describes the relationship between the two lines described below?

Answer 1

If two lines are perpendicular, then the product of their slopes is equal to -1.

If two lines are parallel, then their slopes are equal.

Write the equation of the lines P and Q in slope-intercept form by isolating y. Compare their slopes to see if they are either parallel or pependicular, or none.

The equation of a line with slope m and y-intercept b in slope-intercept form, is:

`y=mx+b`

Line P:

`\begin{gathered} 6x+3y=12 \\ \Rightarrow3y=-6x+12 \\ \Rightarrow y=(-6x+12)/(3) \\ \therefore y=-2x+4 \end{gathered}`

Then, the slope of the line P is -2.

Line Q:

`\begin{gathered} -4x=2y-2 \\ \Rightarrow2y=-4x+2 \\ \Rightarrow y=(-4x+2)/(2) \\ \Rightarrow y=-2x+1 \end{gathered}`

Then, the slope of the line Q is -2.

Since both lines have the same slope, then they are parallel.