Introduction to Linear Polynomials Mind Map

A polynomial is an algebraic expression made using variables, constants, coefficients, and non-negative whole number powers of variables. The degree is the highest power of the variable present in the polynomial.

First arrange mentally by powers of the variable, then identify the highest exponent. Do not use the coefficient to decide the degree.

A linear polynomial in one variable is a polynomial of degree 1, usually written as ax + b, where a and b are constants and a is not equal to 0.

When finding the zero, write p(x) = 0 first and then solve step by step. Always verify by substitution.

A linear polynomial or linear equation in two variables has the form ax + by + c = 0, where x and y are variables, a, b, and c are constants, and a and b are not both zero.

Substitute x and y in the correct order. The first coordinate is x and the second coordinate is y.

Solving linear polynomials means finding the value or values of variables that make the given linear equation true. At this level, substitution, simple elimination, and verification are useful methods.

After solving, substitute the values in the original equation or equations, not only in your last working line.

Graphical visualisation means representing the solutions of a linear equation in two variables as points on the Cartesian plane. These points lie on a straight line.

Use at least two correct points to draw a straight line, and label axes, scale, points, and the equation of the line.

A real-world linear relationship is a situation where two quantities change at a constant rate and can be represented by a linear equation such as ax + by = c or y = mx + b.

Before forming the equation, write what each variable represents and keep units consistent.

Horizontal lines have equations of the form y = k, where y stays constant. Vertical lines have equations of the form x = h, where x stays constant.

If y is constant, the line is horizontal. If x is constant, the line is vertical.

The intersection of two linear graphs is the point where the two lines meet. Algebraically, it represents the common solution of the two linear equations.

Always verify the intersection point in both equations, especially if the graph scale is small.