Write an equation

Question

write an equation of the line parallel to the line x+2y=6 and containing the point (-6,6) write the answer in standard form 

Answer 1

Hi Jennifer.

 

To write the equation of a line that is parallel to the given line, you need to determine the slope of the given line.  The slope of the parallel line will be the same.

 

Put it in y = mx + b  form   and then the slope, m, is just the number "x" is multiplied by (the coefficient of "x").

 

x + 2y = 6

 

subtract x from both sides

 

2y = -x + 6

 

divide both sides by 2

 

y = -(1/2)x + 3

 

So the slope of the given line  is -(1/2).   The parallel line will have the same slope, -(1/2)

 

Now you are tasked with finding the equation of a line with a slope of -(1/2) and going through the point (-6,6).

 

 

Answer 2

x + 2y = 6     Subtract x from both sides.

2y = -x + 6   Divide both sides by 2.

y = -1/2 x + 3    So, the slope = -1/2.

Parallel lines have the same slope. So, the slope of the new line will also be 1/2.

Since you have a point and a slope, use the point-slope form for the equation of a line.

y - y₁ = m(x - x₁)    P(-6,6)

y - 6 = -1/2 (x +6)      Multiply both sides by -2.

-2y + 12 = x + 6   Add 2y and subtract 12 from both sides.

0 = x + 2y - 6

 

Answer 3

Now, you may convert the equation x+2y=6 to slope-intercept form (y=mx+b) and get y=-(1/2)x+3, or

you might convert Ax+By = C to slope-intercept form and get y = (-A/B)+C/A  and realize that all parallel lines have a Standard Form that looks like x+2y=C.  Insert the coordinates of the point to find C.

 

      (-6) + 2(6) = C

        -6 + 12 = C

           6 = C

 

The parallel line is x+2y=6           [Standard Form looks like Ax+By=C]

 

Oops! that's the same equation (and the same line), so the point (-6,6) must be on the original line !