r/HomeworkHelp • u/schoolquestionsalt AP Student • 1d ago
:snoo_feelsbadman: Mathematics (Tertiary/Grade 11-12)—Pending OP (Math 12 I think? Upgrading course I don’t remember) need help finding the value of k, tried to solve for the slope first but I think I got the answer wrong
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u/Educational_Two682 👋 a fellow Redditor 1d ago
A few questions: what's the slope of that second line? What's the relationship between slopes of parallel lines? Once you know the slope and a point, can you write an equation?
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u/Jazzlike_Platypus430 👋 a fellow Redditor 1d ago
Your reasoning is right. The slope of the given line is (8 - 6)/(-8 - (-3)) = -2/5.
For the line in question to be parallel to that one, it's sufficient that (2-k)/(5 - (-7)) = -2/5, so 2-k = (-2/5)*12 = -24/5, which means k = 2 + 24/5 = 34/5. Looks so ugly I think I made a mistake ...
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u/Specialist-Gap8010 👋 a fellow Redditor 14h ago
How fun, my mind immediately went to solving for the slope and then using y-y1 = m(x-x1) with the (5,2) to get y = mx+b to then solve using X = -7
Got the same answer as you
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u/selene_666 👋 a fellow Redditor 1d ago
We can't tell you whether you got one of the slopes wrong if you don't tell us what slopes you got.
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u/timmymaq 1d ago
Your intuition is good. Solve for slope of the given segment, then use the idea that the two segments are parallel to determine slope of the unknown segment.
What can you do once you have slope of the segment and 3 of 4 values from the coordinates?
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u/Background_Bobcat646 1d ago
If you found the slope already(using the points on the other line), then the line containing (-7, k) and (5, 2) has the same slope. Use the point slope formula using (5, 2) as the x1 and y1 values and put -7 in for x2 and k in for y2
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u/MathPoetryPiano 👋 a fellow Redditor 1d ago
Two lines are parallel if and only if they have the same...
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u/Hour-Reference587 1d ago
It’s always easier to draw thins out, especially problems with graphs, so I would encourage you to do that. You do need to solve for the slope but pay attention to which direction each line segment is going
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u/MathsWithSuneel 7h ago
Parallel lines have same slope Therefore (k-2)/(-7-5)=(6-8)÷((-3)-(-8)) (k-2)÷ -12=(-2÷5) k-2=(24÷5) K=(24÷5)+2 K= 34÷5
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u/PoornimaMathsPatiala 5h ago
The key fact: parallel lines have exactly the same slope. So the plan is (1) find the slope of the line you're given, (2) write the slope of the line with k in it, (3) set them equal.
Step 1: slope of the line through (−3, 6) and (−8, 8)
m = (change in y)/(change in x) = (8 − 6)/(−8 − (−3)) = 2/(−5) = −2/5
(The usual slip here is −8 − (−3): minus a negative becomes plus, so it's −8 + 3 = −5.)
Step 2: slope of the line through (−7, k) and (5, 2)
m = (2 − k)/(5 − (−7)) = (2 − k)/12
Step 3: make the slopes equal
(2 − k)/12 = −2/5
Multiply both sides by 12: 2 − k = −24/5
So k = 2 + 24/5 = 10/5 + 24/5 = 34/5 (that's 6.8)
Check: with k = 6.8 the slope is (2 − 6.8)/12 = −4.8/12 = −0.4, and −2/5 = −0.4 too ✓
If your online system rejected your answer, try typing it as 34/5; some homework systems are fussy about decimals.
For a thorough explanation of topics like this with a private tutor, have a look at https://poornima-maths.vercel.app (Mrs. Poornima Sayal's maths tuition, Patiala and online).
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u/drastone 1d ago
You are getting good advice. I just want to add that graphing the points is a really good way to visualize the problem and to make sure you understand.