91Ó°ÊÓ

The y-intercept is where the line crosses the y-axis. In the slope-intercept form of a linear equation, which is \[ y = mx + b \], the y-intercept is represented by the \( b \) value.
In our given equation \( y = -2x + 3 \), the y-intercept is 3. This tells us that the line crosses the y-axis at the point (0, 3).
This point is important because it gives us a precise starting location on our coordinate plane. No matter the slope, every linear equation in slope-intercept form will cross the y-axis at a particular point. Understanding this allows us to start plotting our graph with confidence.
To find it:

• Identify the \( b \) in the equation.
• Mark the point on the y-axis that corresponds to this value.

After identifying and plotting the y-intercept, you can then use the slope to determine other points for the line.

The slope of a line describes how steep the line is. It is the \( m \) value in the slope-intercept equation \[ y = mx + b \].
In the equation \( y = -2x + 3 \), the slope is -2. This means for every 1 unit increase in \( x \), the \( y \) value decreases by 2.
Understanding the slope helps us plot the direction and steepness of the line. It can be seen as a ratio:

• Rise/Run
• Vertical change/Horizontal change

For a slope of -2:

• Move 1 unit to the right (positive direction of \( x \)).
• Move 2 units down (negative direction of \( y \)).

This gives us another point on the line. Using the y-intercept and the slope, we can plot this second point to help draw the line accurately.

The coordinate plane, also known as the Cartesian plane, consists of two perpendicular lines called axes:

• The horizontal axis is the x-axis.
• The vertical axis is the y-axis.

These axes intersect at the origin, which is (0,0).
Each point on the coordinate plane is represented by an ordered pair (\( x \), \( y \)). The x-value shows the position along the x-axis, and the y-value shows the position along the y-axis.
For graphing purposes, it is essential to understand how to:

• Plot points using ordered pairs.
• Identify the positions relative to the x-axis and y-axis.

When graphing a line, start by plotting the y-intercept on the y-axis. Then, use the slope to determine additional points by moving along the x-axis and making corresponding adjustments on the y-axis.
Understanding the coordinate plane layout allows us to plot the line accurately and interpret its behavior efficiently.