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# core 1 question ?

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1. The gradient of the line perpendicular to 2y=cx-3 is -2. Find C?
2. (Original post by Chelsea12345)
The gradient of the line perpendicular to 2y=cx-3 is -2. Find C?
Yeah, so if the gradient perp to this line is -2, then the gradient of this line must be 1/2. Get this line in the form of y=mx+c then do m=1/2 and solve for c.
3. (Original post by Chelsea12345)
The gradient of the line perpendicular to 2y=cx-3 is -2. Find C?
1. Rewrite in the form
2. Use the fact that if two perp. lines have gradients then
4. Rearrange equation into the form y=mx+c, input your gradient into the equation (it will not be -2, rather the reciprocal) and then you should get a value for c.
5. (Original post by RDKGames)
Yeah, so if the gradient perp to this line is -2, then the gradient of this line must be 1/2. Get this line in the form of y=mx+c then do m=1/2 and solve for c.
i got the first bit but how do i solve for C? do i put the gradient back into the equation or something?
6. (Original post by Chelsea12345)
i got the first bit but how do i solve for C? do i put the gradient back into the equation or something?
You create a linear equation with C being the only unknown and you solve for it. No substitution needed.
7. (Original post by RDKGames)
You create a linear equation with C being the only unknown and you solve for it. No substitution needed.
Thankyou!
8. (Original post by natsciguy)
A line perpendicular to a line always has a negative reciprocal gradient.

If the gradient of the line is -2, then the negative reciprocal is -1/-2 or 1/2.

To get the equation in standard form (y=mx+c) we must divide through by 2 to get y=c/2x-1.

As c/2 is the gradient (as it is the coefficient of x) then 1/2=c/2. Therefore c=1.
Full solutions are not allowed

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