Build a Polynomial
Slide each coefficient and watch the expression, its terms, and its degree update live.
TermEach piece of the expression separated by + or − is a term. Sliding a coefficient to 0 removes that term.
CoefficientThe number multiplying a variable, like the 2 in 2x. It can be positive, negative, or zero.
ConstantA term with no variable attached — it never changes as x changes.
DegreeThe highest power of the variable that actually appears (with a non-zero coefficient).
Degree 0 = constant · Degree 1 = linear · Degree 2 = quadratic · Degree 3 = cubic.
The Input–Output Machine
A linear polynomial turns every input x into one output y = ax + b.
x = 4
➜
y = 2x + 3
➜
y = 11
FunctionA rule like y = ax + b that turns every input x into exactly one output y.
Linear patternLook at the table: each time x goes up by 1, y changes by the same amount — that constant amount is a.
Try changing the slope a and watch how much the output jumps between consecutive rows.
Linear Growth & Decay
A linear pattern changes by the same amount at every step. Is it growing, shrinking, or staying flat?
Linear growthThe value increases by the same fixed amount at every step. The line slopes upward.
Linear decayThe value decreases by the same fixed amount at every step. The line slopes downward.
Linear patternA sequence where the difference between consecutive terms stays constant — that constant is the common difference.
Slope and Y-Intercept
Every line y = ax + b is set by two numbers: its slope a and where it crosses the y-axis, b.
Slope (a)How steep the line is. Positive a: line rises left to right. Negative a: line falls. Bigger |a| means steeper.
Y-intercept (b)Where the line crosses the y-axis, at the point (0, b).
Parallel linesLines with the same slope a but different b are parallel — same tilt, different crossing point.
Keep a fixed and drag b — the line shifts up and down but stays equally tilted.