Respuesta :
we have the following set of equations,
[tex]\begin{gathered} 1)y=-2x+6 \\ 2)y=\frac{1}{2}x+3 \\ 3)2x+4y=8 \end{gathered}[/tex]We need them in slope-intercept form, therefore,
Line 1)
[tex]y=-2x+6[/tex]Line 2)
[tex]y=\frac{1}{2}x+3[/tex]Line 3)
[tex]\begin{gathered} 2x+4y=8 \\ 4y=-2x+8 \\ y=-\frac{2}{4}x+\frac{8}{4} \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]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.
