Question

The equations of three lines are given below.Line 1: y=5/2x-7Line 2: 10x-4y = -2Line 3: 2y = 5x+7For each pair of lines, determine whether they are parallel, perpendicular, or neither.

Answer 1

We have the following set of equations,

`\begin{gathered} y=(5)/(2)x-7 \\ 10x-4y=-2 \\ 2y=5x+7 \end{gathered}`

To know whether they are parallel or perpendicular we need to have all three equations in slope-intercept form, or

`y=mx+b`

Line 1,

`y=(5)/(2)x-7`

Line 2,

`\begin{gathered} 10x-4y=-2 \\ -4y=-2-10x \\ y=-(10x)/(-4)-(2)/(-4) \\ y=(5)/(2)x+(1)/(2) \end{gathered}`

Line 3,

`\begin{gathered} 2y=5x+7 \\ y=(5)/(2)x+(7)/(2) \end{gathered}`

Notice, all three lines have a slope of m = 5/2

Since the slopes are all the same, all three lines are parallel