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
For more information, refer to the link given below:
https://brainly.com/question/11528842
