A line passes through (2, 2) and is perpendicular to the line 3x + y =

1.	A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept isA. 1/3B. 2/3C. 1D. 4/3
Answer» Given line is 3x + y = 3 Now, we find the slope of given equation 3x + y = 3 It can be re-written as y = -3x + 3 Since, the above equation is in y = mx + b form So, the slope m = -3 Slope of perpendicular line = 1/3 So, the line passes through (2, 2) and having slope 1/3 is y - 2 = 1/3(x - 2) ⇒ 3y – 6 = x – 2 ⇒ 3y = x + 4 y = 1/3x + 4/3 [∵y = mx + c] So, the y – intercept is 4/3 Hence, the correct option is (d)

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept isA. 1/3B. 2/3C. 1D. 4/3

Answer»

Given line is 3x + y = 3

Now, we find the slope of given equation 3x + y = 3

It can be re-written as y = -3x + 3

Since, the above equation is in y = mx + b form

So, the slope m = -3

Slope of perpendicular line = 1/3

So, the line passes through (2, 2) and having slope 1/3 is

y - 2 = 1/3(x - 2)

⇒ 3y – 6 = x – 2

⇒ 3y = x + 4

y = 1/3x + 4/3 [∵y = mx + c]

So, the y – intercept is 4/3

Hence, the correct option is (d)