Graphing from slope and intercept
A line given by slope and y-intercept is usually written in the form (y = mx + b), where (m) is the slope and (b) is the y-intercept.
Step-by-step method
- Find the y-intercept: The value (b) tells you where the line crosses the y-axis. Plot the point ((0, b)).
- Use the slope: The slope (m) tells you how to move from that point.
- If (m = \frac{\text{rise}}{\text{run}}), move up or down for the rise and right or left for the run.
- Positive slope goes up as you move right; negative slope goes down as you move right.
- Plot a second point: Starting at the y-intercept, use the slope to locate another point.
- Draw the line: Connect the points with a straight line and extend it in both directions.
Helpful check
Make sure the line crosses the y-axis at the correct intercept and has the correct steepness and direction. If needed, test another point by reading it from the graph and checking whether it matches the equation.
Common mistakes
- Mixing up rise and run
- Starting at the wrong intercept
- Forgetting that a negative slope changes direction
Use the intercept first, then the slope, and your graph will match the equation.