# How do you write an equation of a line that is parallel to y+3x=7 and passes through point (7,2)?

Feb 9, 2015

I would use first your equation to find the SLOPE of your line. Basically the slope is a number that tells you what the inclination of your line is.
So, to find the parallel to your line you need a line with the same inclination...the same slope:
Your line: $y + 3 x = 7$ can be written (isolating the $y$ on the left) as:
$y = - 3 x + 7$ this allows you to "read" immediately the slope of your line, the coefficient of $x$, which in your case is $- 3$.

Now the difficult bit...
The slope represents the inclination of your line and basically tells you how $y$ changes when $x$ changes!

For example, a big slope means that at every fixed change in $x$ the value of $y$ changes a lot and your line is VERY steep!!!
Have a look at this picture:

slope $5$ is steeper than slope $2$!

To find your slope you simply take the change in $y$ divided by the change in $x$:

$s l o p e = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ but you want a slope which is equal to the one of your original line: $- 3$
$s l o p e = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
$- 3 = \frac{y - 2}{x - 7}$
$- 3 x + 21 = y - 2$ and finally your line:
$y + 3 x = 23$