What quantity did you change?
Labs / Mathematics
Linear Equations
Every straight line is a rule: pick an x, multiply by the slope, add the intercept, and you land on the line. Drag the round handle to slide the line up and down, drag the square handle to tilt it, then dial in a target y to solve for x — or switch on a second line and watch where the two cross.
Labs / Mathematics / Linear Equations
Linear Equations
Every straight line is a rule: pick an x, multiply by the slope, add the intercept, and you land on the line. Drag the round handle to slide the line up and down, drag the square handle to tilt it, then dial in a target y to solve for x — or switch on a second line and watch where the two cross.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
y = 1x + 2m 1x-int -2y-int 2meet off
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- What happens to the whole line when the slope m is 0? Where is its x-intercept then?
- Make the slope negative. Which way does the line tip, and does the x-intercept move left or right?
- Set a target y and read off the solution x. How does that x shift as you steepen the slope?
- Turn on the second line. Can you make the two lines never meet — and what do their slopes share when they don't?
- Can you find a slope and intercept that send the line exactly through the point (3, 3)?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.