Two lines are parallel if their slopes are the same
Two lines are perpendicular if the products of their slopes = -1
To get the slopes, we can compare the equation of the line to the general equation of a line in slope-intercept form (y=mx+c)
Looking at the options given
Option 1
Not correct
Option 2
[tex]\begin{gathered} x-y=7 \\ y=x-7 \end{gathered}[/tex]
and
[tex]y=x+3[/tex]
The slope of the two lines = 1
hence, Not correct
Option 3
This option is correct because the plot of the two lines on a graph are perpendicular
The plot is shown below
Option 4
[tex]\begin{gathered} y=-4x+1 \\ \text{slope}=\text{ -4} \end{gathered}[/tex]
for
[tex]\begin{gathered} 8x+2y=-10 \\ \text{make y the subject of the formula} \\ 2y=-8x+10 \\ \text{Divide both sides by 2} \\ y=-4x+5 \end{gathered}[/tex]
Hence, the slope is the same.
so the option is not correct
