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, 1) and parallel to 4x - 3y - 7 = 0

Part B: Passes through (-2, 1) and perpendicular to 4x - 3y - 7 = 0

4x - 3y - 7 = 0

-3y = - 4x + 7

y = 4/3x - 7/3 ... slope here is 4/3

A. a parallel line will have the same slope

y = mx + b

slope (m) = 4/3

(-2,1) ... x = - 2 and y = 1

sub and find b, the y int

1 = 4/3 (-2) + b

1 = - 8/3 + b

1 + 8/3 = b

3/3 + 8/3 = b

11/3 = b

so ur parallel line is : y = 4/3x + 11/3

B. A perpendicular line will have a negative reciprocal slope. To get the negative reciprocal of a number, u flip the number and change the sign. So our perpendicular line will need a slope of - 3/4

y = mx + b

slope (m) = - 3/4

(-2,1) ... x = - 2 and y = 1

sub and find b, the y int

1 = - 3/4 (-2) + b

1 = 3/2 + b

1 - 3/2 = b

2/2 - 3/2 = b

-1/2 = b

so ur perpendicular equation is : y = - 3/4x - 1/2