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Answers:

Explanation:

Parallel lines always have equal slopes, but different y intercepts. For example, the two lines y = 3x+5 and y = 3x+7 have a slope of 3. Refer to y = mx+b where m is the slope. Parallel lines never intersect.

For perpendicular lines, the two slopes always multiply to -1 assuming neither line is vertical nor horizontal. Consider the two linear equations

y = (1/2)x+5

y = -2x-7

The slopes 1/2 and -2 multiply to -1 which is enough to show that they are perpendicular lines. The two lines meet at a 90 degree angle.

To go from one slope to the other, we apply the negative reciprocal. That means we...

Applying the first step to 1/2 gets us 2/1 or 2. Then changing the sign has us go from 2 to -2. This process can be reversed.

For some of these equations, you'll need to rearrange things into either point-slope form or slope intercept form. This will allow you to read off the slope.

Point slope form is y-y1 = m(x-x1)

Slope intercept form is y = mx+b

For either case, all we care about is the variable m.

I'll show how problem 14 transforms into slope intercept form

x+2y = 14

2y = -x+14

y = (-x+14)/2

y = (-x/2) + (14/2)

y = (-1/2)x + 7

We see that m = -1/2 here. Anything parallel to this will have the same slope. The perpendicular slope is 2 after applying the negative reciprocal operation. Problems 13, 15, 16, 17, and 18 are going to follow similar steps.

for parallel slope the slope stays the same. for perpendicular slope changes by flipping and changing the sign. ex: 1/3 --> -3/1 or -2 --> 1/2

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step-by-step explanation: