How do you find the slope and intercept of 4x-2y=12?

Jan 20, 2016

$m = 2$
$a = - 6$
$b = 3$

Explanation:

Given equation is $4 x - 2 y = 12$
Now, general slope equation is $y - {y}_{o} = m \left(x - {x}_{o}\right)$ where $m$ is the slope of the equation.
IF we rearrange the given equation, we see that it becomes
$2 y = 4 x - 12$
Considering ${y}_{o} = 0$, and taking $4$ common in the left hand side and dividing the whole equation by 2, we get what we want. That is
$2 y = 4 \left(x - 3\right)$ Divide by $2$ and
$y = 2 \left(x - 3\right)$.
Comparing the one we solved with the general equation, we see that $m = 2$.

Now, for intercept form equation, the general equation is
$\frac{y}{a} = \frac{x}{b} = 1$ where $a$ is the y-intercept and $b$ is the x-intercept.
So rearranging the original equation we had $4 x - 2 y = 12$ and dividing the equation by $12$, we get
$\frac{x}{3} - \frac{y}{6} = 1$
So $a = - 6$ (since the $y$ parameter has a negative value)
and $b - 3$