Spoiler: you already know more about slopes than you think!
Have you ever walked up a really steep hill and thought “whoa, my legs are burning”? Or coasted down a gentle ramp on your bike? That feeling of steepness — that's slope!
OK so slopes are about steepness. But how do we put a number on it? Here's the trick: count how much it goes UP versus how much it goes ACROSS.
Drag the endpoints on the grid below. Watch the rise and run change!
Ready for the formula? You basically already know it. Slope is just rise ÷ run, written fancy:
Remember tilting that ramp earlier? This formula is just measuring the same thing — how steep something is — but with exact numbers.
Click pairs of points on the graph to draw line segments. Each one gets its own color so you can compare slopes side by side!
Click anywhere to place your first point. Click and drag existing points to move them.
Here's the cool part: slope isn't just about hills. Anytime something changes steadily, you can measure it with slope. Mathematicians call this the “rate of change.”
Think about a gym membership: you pay $15 every month. After 1 month you've paid $15, after 2 months $30, after 3 months $45. If you graph it, you get a straight line with slope = 15. That steady rate IS the slope!
You might have seen this equation before: y = mx + b. It looks fancy, but you already know what the pieces mean!
Drag the sliders to change m and b. Watch how the line moves! Turn on the parallel line to see: same slope = same steepness, just shifted.
Think you've got it? Let's find out. Don't worry — you can try as many times as you want!