# How do you write an equation in standard form for a line passing through (2, -3), m= -3.6?

Apr 8, 2018

$18 x + 5 y = 21$

#### Explanation:

The standard form of a linear equation is $A x + B y = C$.

Since we are given a slope and a point, the slope-intercept form of a linear equation will quickly provide us with an answer.

Recall that any (non-vertical) line can be written in the form $y = m x + b$, where $m$ is our slope and $b$ is our initial value. We find $b$ by plugging in the provided point and slope:

$y = m x + b$
$y = - 3.6 x + b$
$- 3 = - 3.6 \left(2\right) + b$
$- 3 = - 7.2 + b$
$4.2 = b$

Thus, our linear equation in slope-intercept form is $y = - 3.6 x + 4.2$. By moving our term containing $x$ to the left-hand side of the equation, we obtain our equation in standard form:

$y = - 3.6 x + 4.2$
$3.6 x + y = 4.2$

We can clean up our answer by multiplying through by $10$ to remove our decimals, then simplifying.

$3.6 x + y = 4.2$
$36 x + 10 y = 42$
$18 x + 5 y = 21$