The wheelchair ramp
A ramp that rises 1 foot for every 4 feet it runs has a slope of 1/4 — steeper ramps climb faster. In y = mx + b, m is that steepness and b is where the ramp starts off the ground; the whole line is just the ramp's path.
Slope-intercept form
A line can be written y = mx + b, where m is the slope (steepness) and b is the y-intercept (where the line crosses the y-axis).
Slope = rise / run
A slope of 2 means y increases by 2 each time x increases by 1.
Simulation · Line grapher: y = mx + b
y = 1x + 2
Drag the slope and intercept to see how each one moves the line.
Lab · Find the rule
- Set the slope (m) to 2 and the intercept (b) to 1.
- Read the point where the line crosses the y-axis — that's b.
- Move 1 step right and count how many steps up the line goes — that's m.
- Now set m to a negative value and watch the line tilt the other way.
What you should see: The purple dot sits at (0, b) and the line rises by m for every step right. A negative slope falls instead of rises.