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# y-y1 = m(x - x1) ?

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1. Just wondering if anyone could please explain how this equation is derived from y=mx+c and what the advantages are if you use it?

I'm comfortable using this 'new' equations in terms of applying it to questions when I have to, but I'm (annoyingly) a person who likes to understand why you use a formula instead of just being told to use it
2. With , you're essentially translating the graph of the line horizontally with and vertically with .

This form is useful in calculus when finding equations of tangent and normal lines to a certain point on the graph. Rather than finding the value of y at x=0, you just plug in the coordinates of tangency.
3. (Original post by surina16)
Just wondering if anyone could please explain how this equation is derived from y=mx+c and what the advantages are if you use it?

I'm comfortable using this 'new' equations in terms of applying it to questions when I have to, but I'm (annoyingly) a person who likes to understand why you use a formula instead of just being told to use it
If you have the gradient and a point on the line, this new form is quicker than having to solve an equation to find the value of c, as you would do if you used y=mx+c.
It is derived by subbing x1, y1 into y=mx+c to give c = y1-mx1, so y = mx + y1 - mx1 -> y - y1 = mx - mx1 = m(x - x1), as required.
4. The gradient of a line is
As the gradient is constant, we can say
And then multiplying the bottom of the fraction
Which is the same as

A lot of the time this form is better that the main reason is when there is more than 1 y, e.g.
5. (Original post by MartyO)
With , you're essentially translating the graph of the line horizontally with and vertically with .

This form is useful in calculus when finding equations of tangent and normal lines to a certain point on the graph. Rather than finding the value of y at x=0, you just plug in the coordinates of tangency.
You don't need the +c at the end, that comes from when you expand everything as they make up the constant.
6. (Original post by Sal.Tek_ 〔サルテック〕)
The gradient of a line is
As the gradient is constant, we can say
And then multiplying the bottom of the fraction
Which is the same as

A lot of the time this form is better that the main reason is when there is more than 1 y, e.g.
(Original post by HapaxOromenon3)
If you have the gradient and a point on the line, this new form is quicker than having to solve an equation to find the value of c, as you would do if you used y=mx+c.
It is derived by subbing x1, y1 into y=mx+c to give c = y1-mx1, so y = mx + y1 - mx1 -> y - y1 = mx - mx1 = m(x - x1), as required.
(Original post by MartyO)
With , you're essentially translating the graph of the line horizontally with and vertically with .

This form is useful in calculus when finding equations of tangent and normal lines to a certain point on the graph. Rather than finding the value of y at x=0, you just plug in the coordinates of tangency.
Thank you everyone Makes so much sense now

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