Finding the equation of a line

**blame_canada100** · February 12th 2010, 12:39 PM

write the equation of a line that is parallel to 3y+2x=12 and whose y-intercept is 2.

**e^(i*pi)** · February 12th 2010, 12:46 PM

Originally Posted by blame_canada100

write the equation of a line that is parallel to 3y+2x=12 and whose y-intercept is 2.

1. The equation of a straight line is $y = mx+c$ where $m$ is the gradient and $c$ the y intercept

2. If a line is parallel the gradients must be equal.

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Use the two points above to answer the question

Spoiler:

**mr fantastic** · February 12th 2010, 12:46 PM

Originally Posted by blame_canada100

write the equation of a line that is parallel to 3y+2x=12 and whose y-intercept is 2.

The given line has a gradient of $- \frac{2}{3}$ and this will also be the gradient of the required line. Furthermore, you're given the y-intercept of the required line. Now recall that the equation of a line can be written y = mx + c ....

**Plato** · February 12th 2010, 02:14 PM

Here is a quick fix for this problem.
Any line parallel to $2x+3y=12$ has the form $2x+3y=C$ .
Just determine $C$ so that the point $(0,2)$ is on that line.

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