how do you write the equation of a line parallel to the given line & passing through the given point.?

Question

-2x=4y-12.  (6,0)

Answer 1

Hi Stephanie

 

First we will put our equation into slope intercept form ( y = mx + b).

 

-2x = 4y - 12 is equivalent to the equation y = -1/2x + 3 by use of basic algebra.

 

We now have our equation in slope intercept form and now need to find the equation parallel to this line and passing through (6,0).

 

To do this we will use the formula, (y - y₁) = m (x - x₁)

 

Using this formula with our information we get...

 

(y - 0) = -1/2 ( x - 6) --> distribute the -1/2 to the x and the -3... y = -1/2x + 3.

 

We now have our equation of the line which is parallel, having the same slope, to the original equation and passes through the point (6,0).

 

 

Answer 2

Parallel lines have the same slope, so we need to convert the equation to 'slope-intercept form', y = mx + b

 

-2x = 4y - 12

Add 12

-2x + 12 = 4y                or 4y = -2x + 12

Divide by 4

y = (- 1/2) x + 3

The 'new line' needs to have the same slope as shown in the equation, - 1/2 and must pass through (6, 0)

For the slope-intercept form of the new equation, y = 0, m = - 1/2 and x = 6,  so...

y = mx + b

0 = (- 1/2) * 6 + b

0 = - 3 + b

Add 3 to each side.

b = 3

So the equation of the new line is y = (- 1/2)x + 3.

The equations are the same, so the lines are the same line.  

Have a good night, Stephanie.

Mary Ann