What is the equation, in slope-intercept form, of the line that is perpendicular to the line y-4=-2/3(x-6) and passes through the point (-2,-2)

That line is in point-slope form:



Where 'm' is the slope and (x1, y1) is a point on the line.

Perpendicular lines have opposite slopes. To get the opposite, we take the reciprocal and multiply it by -1.



Reciprocal:



Multiply by -1:



We can plug this slope and the point into point-slope form, and then convert it to slope-intercept form.





Negatives cancel out:



Distribute 3/2 into the parenthesis:



Simplify the fraction:



Subtract 2 to both sides: