# How do you write in standard form an equation of the line passing through the given point (-3,3) with the given slope 1?

Apr 1, 2015

Answer: $x - y + 6 = 0$

Why?

Use the general standard form:
$a x + b y + c = 0$

Step1:
in gradient and one point form (also known as point-slope form) you have,
$y - 3 = 1 \cdot \left(x + 3\right)$

Step2:
arranging this you get,
$x - y + 6 = 0$

Apr 1, 2015

$- x + y = 0$

Since $y = m x + n$ can represent any line, we can use it.

$m$ is the slope of our line. The given slope is $1$ so $m = 1$.

So our formula is formed as $y = 1 \cdot x + n$

We can now plug the point to this formula to find the value of $n$

$3 = 1 \cdot \left(- 3\right) + n$
$n = 6$

So $y = x + 6$ represents the line. But we should reform this equality in order to be in the standart form:

$- x + y = 6$ is the standart form ($a x + b y = c$)