What it does
A linear polynomial such as p(x) = 2x − 3 has a graph that is a straight line. This page draws y = mx + c and shows the three things every straight line is built from:
- the slope m, drawn as a little triangle: go a run of 2 to the right and the line goes up (or down) a rise of 2m, so m = rise ÷ run;
- the y-intercept c, where the line cuts the y-axis at (0, c);
- the zero, where the line meets the x-axis: solve mx + c = 0 to get x = −c/m.
A table of values shows that each step of 1 in x adds m to y. It fits the Class 9 Maths chapter introducing linear polynomials, and the straight lines chapter of Class 11, where the Class 11 level adds the angle the line makes with the x-axis and the point-slope, intercept and general forms.
Higher powers and their zeros are in polynomial zeros, two lines meeting are in the linear pairs, and the slope of a curve, not just a line, is the derivative slope.
How to use it
- Move the m and c sliders, or type values (the boxes take any number, beyond the sliders too).
- Or drag the handles on the graph: the one on the y-axis moves the line up and down (changes c); the other one turns it (changes m).
- Read the steps under the graph: slope, y-intercept and the zero, with your numbers.
- Switch the Level to Class 11 for the angle of inclination and the other ways of writing the same line.
A worked example
The page starts with m = 2 and c = −3, so p(x) = 2x − 3.
- The slope triangle has run 2 and rise 4: m = 4 ÷ 2 = 2.
- The line cuts the y-axis at (0, −3).
- Zero: 2x − 3 = 0, so x = 3 ÷ 2 = 1.5. The red dot sits at (1.5, 0).
- In the Class 11 level: θ = tan⁻¹(2) = 63.43°, and the intercept form is x/1.5 + y/(−3) = 1.
Tips
- A positive slope climbs from left to right; a negative slope falls.
- Lines with the same m are parallel; lines with the same c all pass through (0, c).
- A flat line (m = 0) has no zero unless it is the x-axis itself.
Check yourself
Four fresh questions: the zero of a linear polynomial, the slope between two points, a y-value from the equation, and where a line in the form ax + by = c cuts the y-axis. Nothing is saved.
FAQ
Why m and c? It is a convention in Indian and British books. Other countries write y = mx + b or y = ax + b; the ideas are the same.
What about a vertical line? x = 3 is a line, but it is not the graph of a function y = mx + c: its run is 0, so its slope is undefined.
Is this from the NCERT book? It covers the same topic with fibub’s own examples. fibub is not part of NCERT.
Where the numbers come from
- Standard results for straight lines: slope m = rise ÷ run, y-intercept c, zero x = −c/m of the linear polynomial mx + c, angle of inclination θ = tan⁻¹ m, and the point-slope, intercept and general forms. Written for fibub.
- Checked against hand-worked lines (y = 2x − 3: zero 3/2, angle 63.43°; y = −x + 4: zero 4, angle 135°), Python math.atan for 1,000 random slopes, and the two-point slope for random point pairs.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.