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The slope-intercept form is a popular way to write the equation of a line. It is given by the formula: \( y = mx + b \). Here, \( m \) represents the slope of the line, which tells us how steep the line is, while \( b \) signifies the y-intercept, which is where the line crosses the y-axis. This form is extremely useful because it immediately provides two important pieces of information about the line: how it moves and where it starts.
For example, in the equation \( y = x - 4 \), the slope (\( m \)) is 1, indicating a steady, diagonal rise where for each increase in \( x \) by 1, \( y \) also increases by 1.
The y-intercept (\( b \)) is -4, showing us that the line cuts through the y-axis at the point \( (0, -4) \). This makes graphing much easier since we have a starting point and a direction to follow.

A table of values is an essential tool when graphing a linear equation because it helps us to accurately plot points on a graph.
To create a table of values for the equation \( y = x - 4 \), we choose several x-values, then compute their corresponding y-values using the equation.

• Start with different kinds of x-values: negative, zero, and positive.
• Let's take x-values of -2, 1, and 4.
• Plug these into the equation to get y-values:
  • For \( x = -2 \), \( y = -2 - 4 = -6 \).
  • For \( x = 1 \), \( y = 1 - 4 = -3 \).
  • For \( x = 4 \), \( y = 4 - 4 = 0 \).

This gives us the points (-2,-6), (1,-3), and (4,0). These points provide a guide to plot our line on the graph.

Plotting the points is a critical step to visually represent the equation on the graph. Once we have a table of values, it’s time to place these points on a coordinate plane. Here's how we do it:

• First, draw a graph with an x-axis (horizontal) and a y-axis (vertical).
• The origin, where the axes intersect, is (0,0).
• Locate each point from your table of values and mark it clearly on the graph.
• For example, place a point at (-2, -6), followed by a point at (1, -3), and then (4, 0).

Once the points are marked, use a ruler to draw a straight line through them. The line can be extended in both directions to formally represent the graph of the equation \( y = x - 4 \). This step translates numerical work into a clear visual image, which can make understanding the behavior of the equation much easier.