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, 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)

Answer 1

4x - 3y - 7 = 0.....put this in y = mx + b form
-3y = -4x + 7
y = 4/3x - 7/3.....slope here is 4/3.
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A parallel line will have the same slope.

y = mx + b
slope(m) = 4/3
(-2,2)....x = -2 and y = 2
now sub into the formula and find b, the y int
2 = 4/3(-2) + b
2 = - 8/3 + b
2 + 8/3 = b
6/3 + 8/3 = b
14/3 = b
so ur parallel equation is : y = 4/3x + 14/3 <==
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slope = 4/3. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, flip the original slope and change the sign. So we have 4/3.....now we flip it making it 3/4....now we change the sign, making it -3/4. So our perpendicular line will have a slope of -3/4.

y = mx + b
slope(m) = -3/4
(-2,2)...x = -2 and y = 2
now we sub into the formula and find b, the y int
2 = -3/4(-2) + b
2 = 3/2 + b
2 - 3/2 = b
4/2 - 3/2 = b
1/2 = b
so ur perpendicular equation is : y = -3/4x + 1/2 <===