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The slope-intercept form of a linear equation is one of the most commonly used forms in algebra. It's written as _\( y = mx + b \)_.
In this formula:

• _\( m \)_ represents the slope of the line, which shows how steep the line is.
• _\( b \)_ is the y-intercept, showing where the line crosses the y-axis.

To convert an equation to slope-intercept form, solve for _\( y \)_ in terms of _\( x \)_. For instance, let’s take the equation from the exercise:
Start with the original equation:
_\( 5x - 6y = 12 \)_
Subtract _\( 5x \)_ from both sides:
_\( -6y = -5x + 12 \)_
Divide each term by _\( -6 \)_:
_\( y = \frac{5}{6}x - 2 \)_
Now the equation is in slope-intercept form, making it easier to graph!

Once you have the equation in slope-intercept form, plotting points becomes straightforward. The y-intercept, _\( b \)_, is your starting point on the y-axis.
In our example, the y-intercept is _\( -2 \)_.
Plot the point _(0, -2)_ on the y-axis. This is your first point on the graph.
Next, use the slope _\( m \)_. Slope is defined as _rise over run_. It tells you how to move on the graph to get to the next point.
For the slope _\( \frac{5}{6} \)_,:

• Rise 5 units up
• Run 6 units to the right

Starting from _(0, -2)_, moving 5 units up and 6 units right will place you at _(6, 3)_.
Plot this point as well. Now you have two points.

Identifying the slope of a line is easier with the slope-intercept form. The slope, _\( m \)_, tells us how slanted the line is.
Positive slopes indicate a line rising from left to right,
whereas negative slopes indicate a line falling from left to right.
In _\( y = \frac{5}{6}x - 2 \)_, the slope is _\( \frac{5}{6} \)_.
This positive slope means the line will ascend as it moves from left to right.
To comprehend this visually:

• Each time you move 6 units right, the line will rise 5 units.

By understanding and identifying the slope correctly, you can predict the direction and steepness of the line before even plotting it.
Combining this knowledge with the y-intercept, you can draw accurate graphs of linear equations, which is an essential skill in algebra.