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Linear Polynomial Explorer

Polynomials · Class IX

Adjust the slope m and intercept c of y = mx + c to see the line tilt and slide.

1
type a value
-55
0
type a value
-1010
Live values
  • x-intercept (zero of polynomial)0
  • y-intercept0
  • Slope1
xy
  • y = m x + c

Formulas in this lab

  • x-intercept (zero of polynomial)
    x=−c/mx = -c/m
  • y-intercept
    y=cy = c
  • Slope
    mm
Tip: A linear polynomial has exactly one zero , that's where the line crosses the x-axis.

Frequently asked questions

▶What is a linear polynomial?

A linear polynomial has the form $p(x) = mx + c$ where m and c are constants and m is non-zero. Its graph is always a straight line with slope m and y-intercept c. The single zero of the polynomial is $x = -\frac{c}{m}$.

▶How do I use this lab?

Slide m to tilt the line and slide c to move it up or down. Set m = 2, c = -4 to see a line crossing the x-axis at x = 2 and the y-axis at y = -4. Try m = 0 in your head to see why we need m non-zero.

▶Common mistake on this topic

Many students mix up the sign of the zero. The zero of $mx + c$ is $-\frac{c}{m}$, not $\frac{c}{m}$. Always set the polynomial equal to zero and solve carefully before writing the final answer.

▶Where do we see linear polynomials in real life?

An auto-rickshaw fare in many Indian cities is $f = 25 + 12d$, a linear polynomial in distance d. The base fare is c = 25 and the per-km rate is m = 12. The lab makes such fare-vs-distance relationships easy to picture.