Write the equation of the line which passes through (2, –1) and is perpendicular to the line with equation 3y – x = 1.

You can start by swapping the x- and y-coefficients and negating one. In standard form the x-coefficient must be positive, so it is convenient to choose that.

... 3x +y = ??

The ?? is a constant chosen to make sure the line goes through the given point. If you fill in 2 for x and -1 for y, you see what the constant needs to be.

... 3x + y = 3(2) +(-1) = 5

The equation is 3x + y = 5.

the correct answer is option c.   3

step-by-step explanation:

points to remember

equation of the line with coordinates (x₁, y₁) and (x₂, y₂) is given by,

slope m = (y₂ - y₁)/(x₂ - x₁)

from the figure we can see a line with two coordinates given

to find the slope of given line

here   (x₁, y₁)   = (-1, -1 ) and (x₂, y₂) = (1, 5)

slope m = (y₂ - y₁)/(x₂ - x₁)

  = (5 - -1)/(1 - -1)

  = (5 + 1)/(1 + 1)

  = 6/2 = 3

therefore the correct answer is option c.   3