Sketch a graph of the equation. y = 1/3 x - 1

To sketch the graph of the equation $y = \frac{1}{3}x - 1$, follow these steps:

Step 1: Define the Problem

Identify the key components of the equation that need to be addressed:

• The equation is in the form of a linear equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 2: Break Down the Problem

Divide the problem into smaller, manageable parts:

• Determine the slope ($m$) and y-intercept ($b$) of the line.
• Plot the y-intercept on the graph.
• Use the slope to find another point on the line.

Step 3: Apply Relevant Concepts

Use appropriate academic theories or formulas to solve each part of the problem:

• Slope ($m$): The slope is $\frac{1}{3}$, which means for every 3 units you move horizontally to the right, you move 1 unit vertically up.
• Y-intercept ($b$): The y-intercept is $-1$, which means the line crosses the y-axis at (0, -1).

Step 4: Analysis, Verify and Summarize

• Plot the y-intercept: Start by plotting the point (0, -1) on the graph.
• Use the slope: From (0, -1), move 3 units to the right (positive x-direction) and 1 unit up (positive y-direction) to find another point on the line, which is (3, 0).
• Draw the line: Connect these two points with a straight line, extending it in both directions.

Final Answer

The graph of the equation $y = \frac{1}{3}x - 1$ is a straight line with a slope of $\frac{1}{3}$ and a y-intercept at -1. It passes through the points (0, -1) and (3, 0).