What is the equation of a line that contains point (3, –1) and is PERPENDICULAR to 12x + 4y = 8?

x - 3y = 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

12x + 4y = 8 ( subtract 12x from both sides )

4y = - 12x + 8 ( divide all terms by 4 )

y = - 3x + 2 ← in slope- intercept form

with slope m = - 3

Given a line with slope m then the slope of a line perpendicular to it is

= - = - = , thus

y = x + c ← is the partial equation

To find c substitute (3, - 1) into the partial equation

- 1 = 1 + c ⇒ c = - 1 - 1 = - 2

y = x - 2 ← in slope- intercept form

Multiply through by 3

3y = x - 6 ( subtract 3y and add 6 to both sides )

x - 3y = 6 ← in standard form

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step-by-step explanation: