Question

The equations of three lines are given below.Line 1: y= -2x+6Line 2: y=1/2x+3Line 3: 2x+ 4y = 8For each pair of lines, determine whether they are parallel, perpendicular, or neither.

Answer 1

we have the following set of equations,

`\begin{gathered} 1)y=-2x+6 \\ 2)y=(1)/(2)x+3 \\ 3)2x+4y=8 \end{gathered}`

We need them in slope-intercept form, therefore,

Line 1)

`y=-2x+6`

Line 2)

`y=(1)/(2)x+3`

Line 3)

`\begin{gathered} 2x+4y=8 \\ 4y=-2x+8 \\ y=-(2)/(4)x+(8)/(4) \\ y=-(1)/(2)x+2 \end{gathered}`

Perpendicular lines have slopes that are negative reciprocals of one another

Notice that the slope of Line 1, m1= -2, is the negative reciprocal of the slop of Line 2, m2= 1/2

Line 3 in not parallel, nor perpendicular to any line

Answer: Line 1 and Line 2 are perpendicular, but Line 3 is neither parallel nor perpendicular to any one.