91Ó°ÊÓ

In the context of linear equations, the slope and y-intercept are crucial elements. A linear equation typically has the format of \( y = mx + b \). Here, \( m \) represents the slope, while \( b \) indicates the y-intercept.
The **slope** \( m \) tells us how steep the line is. It's the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. For example, a slope of \( \frac{1}{4} \) means that for every 4 units you move horizontally, the line moves 1 unit up.
The **y-intercept** \( b \) is where the line crosses the y-axis. It's the value of \( y \) when \( x \) is 0. In the given exercise, the y-intercept \( b \) is -2, which means the line crosses the y-axis at the point (0, -2).

Plotting points accurately is essential for graphing linear equations correctly. To plot points, you need the coordinates, which are values \((x, y)\) denoting positions on the graph.
**First Point - Y-Intercept**:

• Locate the y-intercept on the graph somewhere along the y-axis.
• For our exercise, plot the point (0, -2) on the y-axis.

**Second Point - Using Slope**:

• Start from the y-intercept.
• Use the slope to find the next point. For the slope \( \frac{1}{4} \): move 1 unit up (rise) and 4 units to the right (run).
• Plot this second point at (4, -1).

These points give a clear idea of how the line should look.

A **linear equation** forms a straight line when graphed. These equations are written in the standard form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
In the given problem, the linear equation is \( y = \frac{1}{4}x - 2 \). Here, the slope is \( \frac{1}{4} \) and the y-intercept is -2. The nature of linear equations makes them predictable and easy to graph once you know the slope and intercept.
**Steps to Graphing a Linear Equation**:

• Identify the slope and the y-intercept.
• Plot the y-intercept on the y-axis.
• Use the slope to find another point on the graph.
• Draw a line through the points.

These steps ensure the linear equation is accurately represented on a graph.