How do you convert from one line equation to another?

[Andy21]

Homework Statement

Show how the equation of a line y-2=4x-4 can be converted into the equivalent line equation of 4x+y-6=0.

Homework Equations

The Attempt at a Solution

The closest I have got to it is 4x-y-2=0 by adding and subtracting terms to both sides.

 

[Mark44]

Homework Statement

Show how the equation of a line y-2=4x-4 can be converted into the equivalent line equation of 4x+y-6=0.

It can't. These two equations aren't equivalent.

y - 2 = 4x - 4
<==> y - 4x + 2 = 0
I got this by adding -4x and +4 to both sides.
This equation is equivalent to the one you show below. Multiply the equation above by -1 on both sides and you'll get an equation that can be rearranged to yours.

Homework Equations

The Attempt at a Solution

The closest I have got to it is 4x-y-2=0 by adding and subtracting terms to both sides.

 

[Andy21]

Thanks for the help. The reason I asked this question is to find the equation of the tangent to the circle (x+3)^2 + (y-1)^2=17 at the point (1,2). I know the answer to this is 4x+y-6=0. Can you explain to me how to get this answer.

 

[Mark44]

That answer is correct. I think you made a mistake in calculating the derivative. The slope of the tangent line at (1, 2) is -4, not 4, as you show.

 

[Andy21]

Yes sorry, what I asked in the original question was wrong. Can you explain how to get the answer 4x+y-6=0 for the equation of the tangent from the circle equation and the point I gave in my previous reply. Thanks.

 

[Mark44]

1. Find dy/dx using the circle equation. I used implicit differentiation.
2. Evaluate dy/dx at (1, 2) to get the slope of the tangent line.
3. Use the slope found in step 2 and the point (1, 2) in the point slope form of the line.