Write an equation for the line that has a y-intercept of 2 and is perpendicular to the line 3x + y = 6.

The equation of the line would be y = 1/3x + 2

Step-by-step explanation:

To find this, we must first solve the original equation for y.

3x + y = 6

y = - 3x + 6

This means the original slope is - 3. Since the original slope is - 3, we know that the perpendicular slope is 1/3. This is because perpendicular slopes are opposite and reciprocal.

Now we use the slope and the intercept in slope-intercept form to get the equation.

y = mx + b

y = 1/3x + 2