# Thread: Finding the equation of a line

1. ## Finding the equation of a line

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

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 $\displaystyle y = mx+c$ where $\displaystyle m$ is the gradient and $\displaystyle c$ 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:
$\displaystyle y = -\frac{2x}{3} + 2$

The given line has a gradient of $\displaystyle - \frac{2}{3}$ 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 ....
Any line parallel to $\displaystyle 2x+3y=12$ has the form $\displaystyle 2x+3y=C$.
Just determine $\displaystyle C$ so that the point $\displaystyle (0,2)$ is on that line.