To graph the line given by the equation \( y = \frac{1}{7}x + 3 \), we can identify the slope and y-intercept from the equation.
Step 1: Identify the slope and y-intercept
- The slope (m) is \( \frac{1}{7} \).
- The y-intercept (b) is \( 3 \).
This means that the line crosses the y-axis at the point (0, 3).
Step 2: Plot the y-intercept
- Start by plotting the point (0, 3) on the graph.
Step 3: Use the slope to find another point
- The slope \( \frac{1}{7} \) means that for every 7 units you move to the right (positive direction on the x-axis), you move up 1 unit (positive direction on the y-axis).
- Starting from (0, 3):
- Move 7 units to the right (to x = 7), and then move up 1 unit (to y = 4). This gives you the point (7, 4).
Step 4: Plot the second point
- Plot the point (7, 4) on the graph.
Step 5: Draw the line
- Draw a straight line through the points (0, 3) and (7, 4). Extend the line in both directions.
To summarize, your graph will have the y-intercept at (0, 3) and another point at (7, 4), creating a line with a slope of \( \frac{1}{7} \).