# Question on gradients of curves

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#1
I'm stuck on b. I looked at solution banks (https://activeteach-prod.resource.pe...b_p1_ex12a.pdf) and they just jumped right into the answer. My question is how did they get there? Was it all just trial and error/mental maths skills? Or is there a method?

EDIT: SOLVED!
Last edited by GogetaORvegito?; 4 weeks ago
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4 weeks ago
#2
(Original post by GogetaORvegito?)
I'm stuck on b. I looked at solution banks (https://activeteach-prod.resource.pe...b_p1_ex12a.pdf) and they just jumped right into the answer. My question is how did they get there? Was it all just trial and error/mental maths skills? Or is there a method?
I guess When you fill in the table in a) you'll spot the x -> gradient relationship is linear. So b) should be easy?
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#3
(Original post by mqb2766)
I guess When you fill in the table in a) you'll spot the x -> gradient relationship is linear. So b) should be easy?
Ah well there goes my confidence. I didn't realize it like that. So if it's linear what does that mean
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4 weeks ago
#4
(Original post by GogetaORvegito?)
Ah well there goes my confidence. I didn't realize it like that. So if it's linear what does that mean
Straight line
For suitable m and c.
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#5
(Original post by mqb2766)
Straight line
For suitable m and c.
Sorry, I don't understand. How do I use this to get 2p - 2 ? I can see that the intercept is -2 at 0 but that's it
Last edited by GogetaORvegito?; 4 weeks ago
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4 weeks ago
#6
(Original post by GogetaORvegito?)
Sorry, I don't understand. How do I use this to get 2p - 2 ?
You have not given the values you got in the table.
But if you plot those points for gradient verses x, you should see the gradient of the line is 2 and the y intercept is -2
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#7
(Original post by mqb2766)
You have not given the values you got in the table.
But if you plot those points for gradient verses x, you should see the gradient of the line is 2 and the y intercept is -2
I did notice the intercept but how do I get the gradient of the line is 2?
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4 weeks ago
#8
(Original post by GogetaORvegito?)
I did notice the intercept but how do I get the gradient of the line is 2?
What happens to the curve gradient when you increase x by 1 (each time)?
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#9
(Original post by mqb2766)
What happens to the curve gradient when you increase x by 1 (each time)?
It's increasing by 2? That's how you know the gradient is constantly changing by 2 and therefore the gradient of the curve is 2?
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4 weeks ago
#10
(Original post by GogetaORvegito?)
It's increasing by 2? That's how you know the gradient is constantly changing by 2 and therefore the gradient of the curve is 2?
The gradient of the line is m=2.
The gradient of the curve is 2x-2
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#11
(Original post by mqb2766)
The gradient of the line is m=2.
The gradient of the curve is 2x-2
Ahhh the gradient of the line is 2. That makes sense, so to find the gradient of the line you just see what all the gradients at each point is changing by cool. Then you pop that and the intercept into the equation y = mx + c. So to get x = p you would just substitute p into it. Thank you so much! You are a life saver! I feel like the npc giving the hero a side quest lmao
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