Respuesta :
Answer:
[tex]y =\frac{7}{8}x + 12[/tex] and[tex]y = -\frac{8}{7}x - 8[/tex]
Step-by-step explanation:
The product of the slopes of the perpendicular lines is -1
Option 1) [tex]y =\frac{7}{8}x + 12[/tex] and[tex]y = -\frac{8}{7}x - 8[/tex]
General equation of line : [tex]y=mx+c[/tex]
Comparing with general equation
Slope of line 1 = [tex]\frac{7}{8}[/tex]
Slope of line 2= [tex] -\frac{8}{7}[/tex]
Now product of slopes = [tex]\frac{7}{8} \times \frac{-8}{7}[/tex]
= [tex]-1[/tex]
Since The product of the slopes of the perpendicular lines is -1
So, [tex]y =\frac{7}{8}x + 12[/tex] and[tex]y = -\frac{8}{7}x - 8[/tex] represent perpendicular lines
Option 2) [tex]y = 5x + 15[/tex] and [tex]y = -5x + 15[/tex]
General equation of line : [tex]y=mx+c[/tex]
Comparing with general equation
Slope of line 1 = 5
Slope of line 2= -5
Now product of slopes = [tex]5 \times -5[/tex]
= [tex]-25[/tex]
Since The product of the slopes of the perpendicular lines is not -1
So, [tex]y = 5x + 15[/tex] and [tex]y = -5x + 15[/tex] does not represents the perpendicular lines.
Option 3) [tex]y = 4x + 9[/tex] and [tex]y = 4x -9[/tex]
General equation of line : [tex]y=mx+c[/tex]
Comparing with general equation
Slope of line 1 = 4
Slope of line 2= 4
Now product of slopes = [tex]4 \times 4[/tex]
= [tex]16[/tex]
Since The product of the slopes of the perpendicular lines is not -1
So, [tex]y = 4x + 9[/tex] and [tex]y = 4x -9[/tex]does not represents the perpendicular lines.
Option 4)[tex]y = 9[/tex] and [tex]y = 18[/tex]
General equation of line : [tex]y=mx+c[/tex]
Comparing with general equation
Slope of line 1 = 0
Slope of line 2=0
Now product of slopes = [tex]0 \times 0[/tex]
= [tex]0[/tex]
Since The product of the slopes of the perpendicular lines is not -1
So,[tex]y = 9[/tex] and [tex]y = 18[/tex] does not represents the perpendicular lines.
