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,

$\begin{gathered} y=\frac{5}{2}x-7 \\ 10x-4y=-2 \\ 2y=5x+7 \end{gathered}$

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,

$y=\frac{5}{2}x-7$

Line 2,

$\begin{gathered} 10x-4y=-2 \\ -4y=-2-10x \\ y=-\frac{10x}{-4}-\frac{2}{-4} \\ y=\frac{5}{2}x+\frac{1}{2} \end{gathered}$

Line 3,

$\begin{gathered} 2y=5x+7 \\ y=\frac{5}{2}x+\frac{7}{2} \end{gathered}$

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

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