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# Straight-line graphs 2 watch

1. The answer to this question is 6, but I honestly have no idea how to solve it?!
'A straight line passes through the points with coordinates(-3,-2),(1,6) and (k,16).
Work out the value of k. You must show all your working.'
2. Find the gradient using the first two co-ordinates, and then substitute back into y=mx+c with known values, then solve for x.
3. (Original post by orderofthelotus)
Find the gradient using the first two co-ordinates, and then substitute back into y=mx+c with known values, then solve for x.
I find the equation for the first the two points, which is y= 2x + c, then what do I need to do?
4. (Original post by BT144)
I find the equation for the first the two points, which is y= 2x + c, then what do I need to do?
Nice, that’s what you should’ve got. Now, you can find a value for c by substituting one set of co-ordinates as your x and y values, and then solving for c. So, say you’re using the first set of co-ordinates, let x=-3, y=-2 and m=2 like you’ve just figured out. Now you can easily get a value for c.

Now that you have a complete equation, you can substitute y for 16 and x for k and then solve for k.
5. (Original post by orderofthelotus)
Nice, that’s what you should’ve got. Now, you can find a value for c by substituting one set of co-ordinates as your x and y values, and then solving for c. So, say you’re using the first set of co-ordinates, let x=-3, y=-2 and m=2 like you’ve just figured out. Now you can easily get a value for c.

Now that you have a complete equation, you can substitute y for 16 and x for k and then solve for k.
And I finally got 6! Thanks a bunch for guiding me through the question.
Is it ok if you help me through another question on this topic?
'Here are two straight lines. AB is parallel to PQ(Passes through 5 on y). The equation of the line AB is y = 4x + 1. Find the equation of the straight line PQ.'
In the question hint, it says:
Find the value of the y-intercept for PQ.
Use y = mx + c to find the equation of PQ.'
6. (Original post by BT144)
And I finally got 6! Thanks a bunch for guiding me through the question.
Is it ok if you help me through another question on this topic?
'Here are two straight lines. AB is parallel to PQ(Passes through 5 on y). The equation of the line AB is y = 4x + 1. Find the equation of the straight line PQ.'
In the question hint, it says:
Find the value of the y-intercept for PQ.
Use y = mx + c to find the equation of PQ.'
Since AB and PQ are parallel, the gradients are both the same.
Secondly, you didn't put up any diagram but I suspect from what you've said is that PQ passes through on the y-axis. So, what's the x-coordinate of this point? Hence the coordinates of this point in the form (a,b) are....?

After those two facts, you have sufficient information to determine the equation of PQ.
7. (Original post by BT144)
And I finally got 6! Thanks a bunch for guiding me through the question.
Is it ok if you help me through another question on this topic?
'Here are two straight lines. AB is parallel to PQ(Passes through 5 on y). The equation of the line AB is y = 4x + 1. Find the equation of the straight line PQ.'
In the question hint, it says:
Find the value of the y-intercept for PQ.
Use y = mx + c to find the equation of PQ.'
For two lines to be parallel, they must have the same gradient, else they will cross each other somewhere. Remember that, it's key for your understanding of this kind of topic in maths, especially if you plan to take maths beyond GCSE.

You've pretty much got the question with just that information.
8. (Original post by orderofthelotus)
For two lines to be parallel, they must have the same gradient, else they will cross each other somewhere. Remember that, it's key for your understanding of this kind of topic in maths, especially if you plan to take maths beyond GCSE.

You've pretty much got the question with just that information.
Spoiler:
Show

y = 4x + 5. Got it! Sorry, should have checked the answer in the first place, thanks though.
9. (Original post by BT144)
Spoiler:
Show

y = 4x + 5. Got it! Sorry, should have checked the answer in the first place, thanks though.

You're welcomeeeeeeeeeeee

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