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

The value of a is -1/3 and this can be determined by using the slope-intercept form and also by using the properties of perpendicular lines.

Given :

Equations of lines -- (y = 3x - 1) and (y = ax + 2)

The following steps can be used in order to determine the value of 'a':

Step 1 - Compare the given equation of lines by the slope-intercept form in order to determine the slope of the given lines. The slope-intercept form is given by the equation (y = mx + c).

Step 2 - The value of the slope of the line (y = 3x - 1) is given by:

m = 3

Step 3 - The value of the slope of the line (y = ax +2) is given by:

m' = a

Step 4 - Remember when the two lines are perpendicular to each other than the product of their slopes is equal to -1.

mm' = -1

Step 5 - Substitute the values of slope m and m' in the above expression.

mm' = 3a = -1

a = -1/3

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step-by-step explanation: