Question

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 

Answer 1

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