Thread: Finding the equation of a line

1. Finding the equation of a line

Hello, i was wondering if somebody could tell me what i am doing wrong and which method I should use.
'Find the equation of the line through (-2,1) parallel to y=1/2x-3. Give your answer in the form ax+by=c.
(Method 1) As the equation of the line given has a gradient of 1/2, I know y=1/2x+c. Putting in the x and y coordinates, 1=1/2(-2)+c. Therefore 1=-1+C. This means C is 2. However, I don't know how to put this information into the form ax+by=c, so I am left with y=1/2x+2.
The second method I used was using the equation y-y1=m(x-x1). So y-1=1/2(x+2). 2y-2=x+2 This means 2y-x-4=0, so c=-4. In the right format, the answer would be -x+2y=-4. However, the answer in the textbook is x-2y=-4. Does anybody know where I have went wrong? Any help is much appreciated

2. Re: Finding the equation of a line

Originally Posted by Simon123456
Hello, i was wondering if somebody could tell me what i am doing wrong and which method I should use.
'Find the equation of the line through (-2,1) parallel to y=1/2x-3.
You mean y= (1/2)x- 3, not y= 1/(2x)- 3, right?

(Method 1) As the equation of the line given has a gradient of 1/2, I know y=1/2x+c. Putting in the x and y coordinates, 1=1/2(-2)+c. Therefore 1=-1+C. This means C is 2. However, I don't know how to put this information into the form ax+by=c, so I am left with y=1/2x+2.
One way is to subtract (1/2)x from both sides. That gives (-1/2)x+ y= 2. Multiplying both sides by 2 gives -x+ 2y= 4

The second method I used was using the equation y-y1=m(x-x1). So y-1=1/2(x+2). 2y-2=x+2
This means 2y-x-4=0, so c=-4.
No, adding 4 to both sides gives 2y- x= 4 (not -4) so this would be -x+ 2y= 4 or (multiply both sides by -1) x- 2y= -4.

In the right format, the answer would be -x+2y=-4. However, the answer in the textbook is x-2y=-4. Does anybody know where I have went wrong? Any help is much appreciated

3. Re: Finding the equation of a line

Your first attempt is absolutely right.
You got y = 1/2 x +2 . Multiply both sides be 2 we get
2y = x + 4 Now add -x on both sides and we get
-x + 2y = 4