show all work to write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b is the y-intercept:

part a: passes through (−2, 2) and parallel to 4x − 3y − 7 = 0 (2 points)

part b: passes through (−2, 2) and perpendicular to 4x − 3y − 7 = 0 (2 points)

Part A
The given line passes through (-2,2) and it is parallel to the line



We need to determine the slope of this line by writing it in slope -intercept form.




The slope of this line is


The line parallel to this line also has slope



The equation is



We substitute (-2,2)





The required equation is



PART B

The given line is



The slope of this line is


The slope of the line perpendicular to it is



The equation of the line is



We substitute the point, (-2,2)







The equation of the perpendicular line is