How do you convert from one line equation to another?

In summary, to convert the equation of a line y-2=4x-4 into the equivalent equation of 4x+y-6=0, add and subtract terms to both sides until it is rearranged to the desired form. Additionally, to find the equation of the tangent to a circle at a given point, use implicit differentiation to find dy/dx, evaluate it at the given point to find the slope, and then use the point slope form of a line to form the equation.
  • #1
Andy21
20
0

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.
 
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  • #2
Andy21 said:

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.
Andy21 said:

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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 

FAQ: How do you convert from one line equation to another?

What is a "line equation"?

A line equation is a mathematical representation of a straight line on a graph. It is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

How do I convert from slope-intercept to standard form?

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), multiply both sides of the equation by the denominator of the slope. Then, move the x term to the left side and the y term to the right side, and combine like terms.

3. What is the process for converting from point-slope to slope-intercept form?

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), first solve for y by adding y1 to both sides of the equation. Then, simplify to get the equation in the form y = mx + b.

4. Can I convert from one line equation to another without graphing?

Yes, it is possible to convert from one line equation to another without graphing. This can be done by using algebraic methods, such as solving for y and rearranging the equation, as described in the previous questions.

5. Is there a specific order in which I should convert line equations?

No, there is no specific order in which you should convert line equations. The method you use will depend on the specific forms of the equations you are working with. It may be helpful to simplify the equation as much as possible before converting to a different form.

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