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

Concept:

• Slope intercept form of line: y = mx + c, Where ‘m’ is the slope of the line and ‘c’ is the y-intercept.
• The "point-slope" form of the equation of a straight line is: y - y₁ = m(x - x₁)
• When two lines are perpendicular, the product of their slope is -1.
• If m is the slope of a line, then the slope of a line perpendicular to it is -1/m.

Calculation:

Given: 3x + y = 3

⇒ y = -3x + 3

The slope of line = m = -3

Then the slope of a line perpendicular to it is -1/m = 1/3

The equation of line passing through (2, 2) with slope "1/3" is

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

⇒ 3y - 6 = x - 2

⇒ 3y = x + 4

\(\Rightarrow {\rm{y}} = {\rm{\;}}\frac{1}{3}{\rm{x}} + {\rm{\;}}\frac{4}{3}\)

So, the y-intercept of line is 4/3