91Ó°ÊÓ

When you're working with linear equations, it's super helpful to use the slope-intercept form. This is usually written as \( y = mx + b \).
The \( m \) represents the slope of the line, while the \( b \) is its y-intercept.
How do you get the equation into this form? It's pretty simple. Just solve for \( y \).
Let's take the equation given in the problem: \( \frac{1}{2} x + y = 3 \).
First, subtract \( \frac{1}{2} x \) from both sides to isolate \( y \):
\( y = - \frac{1}{2}x + 3 \).
Now it’s in the slope-intercept form where \( m = -\frac{1}{2} \) and \( b = 3 \).
This form makes it really easy to figure out the slope and the y-intercept, which are essential for graphing the line.

Plotting points is like putting pins on a map to show locations. It's an essential step in graphing any equation.
To start, we identify our first point: the y-intercept. In our equation \( y = -\frac{1}{2} x + 3 \), the y-intercept is \( 3 \).
That's because when \( x = 0 \), \( y = 3 \).
So, you plot the first point at \( (0, 3) \) on the y-axis.
Next, use the slope to find another point on the line.
The slope \( -\frac{1}{2} \) means for every 2 units you move to the right on the x-axis, you move 1 unit down on the y-axis.
Starting from \( (0, 3) \), move right 2 units to \( 2 \) and move 1 unit down to \( 2 \).
Plot this second point at \( (2, 2) \).
These two points are enough to draw a line, but you can plot more if you want to be extra sure.

Understanding the slope and y-intercept is key to mastering linear equations.
The slope indicates how steep a line is and its direction (up or down).
For the equation \( y = -\frac{1}{2}x + 3 \), the slope is \( -\frac{1}{2} \).
This negative slope means the line is going downward as it moves to the right.
The y-intercept is where the line crosses the y-axis.
In our example, the y-intercept is \( 3 \), meaning the line crosses the y-axis at the point \( (0, 3) \).
By understanding both the slope and y-intercept, you can quickly and accurately graph any linear equation.
Simply start at the y-intercept, then use the slope to determine the direction and steepness of the line.