Question

The lines y=3x-1 and y=ax+2 are perpendicular if a=___

Answer 1

Answer:

$a = \frac{-1}{3}.$

Step-by-step explanation:

The equation of line in the form .

y = mx + c

Where m is the slope and c is the y- intercept .

As given

The lines y=3x-1 and y=ax+2 are perpendicular .

Here 3 is slope for equation of line  y=3x-1 and a is slope for equation of line

y=ax+2 .

Now by using properties of the perpendicular lines property .

When two lines are perpendicular than slope of one line is negative reciprocal of the other line .

Thus

$a = \frac{-1}{3}$

Therefore $a = \frac{-1}{3}.$

Answer 2

To find the perpendicular slope, you find the reciprocal  of the slope (in this case, 1/3) and multiply that by -1 (in this case, it gets -1/3)