# How do you graph using slope and intercept of 6x - 12y = 24?

Mar 13, 2018

Re-arrange the equation to get the base form of y=mx+b (slope-intercept form), build a table of points, then graph those points.

graph{0.5x-2 [-10, 10, -5, 5]}

#### Explanation:

The slope-intercept line equation is $y = m x + b$, where m is the slope and b is the point where the line intercepts the y-axis (a.k.a. the value of y when x=0)

To get there, we'll need to rearrange the starting equation some. First off is to move the 6x to the right-hand side of the equation. We'll do that by subtracting 6x from both sides:

$\cancel{6 x} - 12 y - \cancel{6 x} = 24 - 6 x \Rightarrow - 12 y = 24 - 6 x$

Next, we'll divide both sides by y's coefficient, -12:

$\frac{\cancel{- 12} y}{\cancel{- 12}} = \frac{24}{- 12} - \frac{6 x}{- 12} \Rightarrow y = 0.5 x - 2$

Now we have our slope intercept form of the equation, $y = 0.5 x - 2$.

Next, let's build a table of points to plot. Since it's a straight line, we only need 2 points that we can line up with a ruler and draw a straight line through.

We already know one point, which is the y-intercept (0,-2). Let's pick another point, at $x = 10$:

$y = 0.5 \times \left(10\right) - 2$
$y = 5 - 2 \Rightarrow y = 3$

So our second point is (10,3). Now we can draw a straight line that passes through both of those points:

graph{0.5x-2 [-10, 10, -5, 5]}

Mar 13, 2018

$y = \frac{1}{2} x - 2$

#### Explanation:

First you have to get the y by itself so you subtract 6x from both sides $- 12 y = 24 - 6 x$
Then, you want to get one y so you divide both sides by -12
$y = \frac{1}{2} x - 2$
You then graph it so that the y-intercept is at -2, because at the y-intercept, x is always 0. And then you go up 1, over 2 every point after that.