Question

9. Which pair of equations below represent perpendicular lines?

Answer 1

A is correct. ...................................................

Answer 2

Answer:

$y =\frac{7}{8}x + 12$ and$y = -\frac{8}{7}x - 8$

Step-by-step explanation:

The product of the slopes of the perpendicular lines is -1

Option 1) $y =\frac{7}{8}x + 12$ and$y = -\frac{8}{7}x - 8$

General equation of line : $y=mx+c$

Comparing with general equation

Slope of line 1 = $\frac{7}{8}$

Slope of line 2= $-\frac{8}{7}$

Now product of slopes = $\frac{7}{8} \times \frac{-8}{7}$

                                      = $-1$

Since The product of the slopes of the perpendicular lines is -1

So, $y =\frac{7}{8}x + 12$ and$y = -\frac{8}{7}x - 8$ represent perpendicular lines

Option 2) $y = 5x + 15$ and  $y = -5x + 15$

General equation of line : $y=mx+c$

Comparing with general equation

Slope of line 1 = 5

Slope of line 2= -5

Now product of slopes = $5 \times -5$

                                      = $-25$

Since The product of the slopes of the perpendicular lines is not -1

So, $y = 5x + 15$ and  $y = -5x + 15$ does not represents the  perpendicular lines.

Option 3) $y = 4x + 9$ and $y = 4x -9$

General equation of line : $y=mx+c$

Comparing with general equation

Slope of line 1 = 4

Slope of line 2= 4

Now product of slopes = $4 \times 4$

                                      = $16$

Since The product of the slopes of the perpendicular lines is not -1

So, $y = 4x + 9$ and $y = 4x -9$does not represents the  perpendicular lines.

Option 4)$y = 9$ and $y = 18$

General equation of line : $y=mx+c$

Comparing with general equation

Slope of line 1 = 0

Slope of line 2=0

Now product of slopes = $0 \times 0$

                                      = $0$

Since The product of the slopes of the perpendicular lines is not -1

So,$y = 9$ and $y = 18$ does not represents the  perpendicular lines.