Linear Function Lab: Change Slope and Intercept
Explore a linear function by changing slope, intercept, and input. Read its value, zero, and rise over run on a labeled grid.
Free, with no sign-up.
For High school students and adults reviewing the topic.
About 7 minutes.
How does it work?
- Set the slope and vertical intercept, then choose an input x.
- Compare the line with the marked input and output, or open a preset.
- Use the output table to check the challenges.
What will you get?
Connect the coefficients of a straight line with its graph and intercepts.
What does the model assume?
- The rule is y = mx + b over all real inputs, using the school-algebra meaning of linear.
- All coordinates are dimensionless and illustrative. The grid displays x from −10 to 10 and y from −60 to 60.
- Rise is the output change for a run of one input unit. Changing the display scales does not change that ratio.
- A horizontal line with a nonzero intercept has no x-intercept. If both slope and intercept are zero, every x is a zero.
- An x-intercept outside the displayed window still belongs to the full line.
Which setup would you like to try?
What can you change?
Range: -5 to 5 .
Range: -10 to 10 .
Range: -10 to 10 .
What does the model predict?
| Quantity | Value | Unit |
|---|---|---|
| Output y | 7.0000 | |
| x-intercept | -0.5000 | |
| Zero status | One x-intercept | |
| Rise | 2.0000 | |
| Run | 1.0000 |
Solid line: function. Circle: evaluated point. Dashed lines: coordinate guides.
Can you reach these targets?
Make the line pass through (1, 3) and (3, 7), then set x to 3.
- Target: Slope m = 2 ; tolerance 0 .
- Target: Vertical intercept b = 1 ; tolerance 0 .
- Target: Input x = 3 ; tolerance 0 .
- Target: Output y = 7 ; tolerance 0.001 .
Use a slope of −2 and make the line cross the horizontal axis at x = 4.
- Target: Slope m = -2 ; tolerance 0 .
- Target: x-intercept = 4 ; tolerance 0.001 .