Introduction to Linear Polynomials

A linear polynomial ax + b has degree 1. Its graph is a straight line; a tells how steep it is and b where it crosses the y-axis.

Key ideas

• A linear polynomial is ax + b with a ≠ 0; its degree is 1.
• The value of p(x) at x = k is found by putting k in place of x.
• The zero of ax + b is the x that makes it 0: x = −b/a. A linear polynomial has exactly one zero.
• The graph of y = ax + b is a straight line. The zero is where the line crosses the x-axis.
• a is the slope: y changes by a each time x goes up by 1. b is the y-intercept.
• Lines with the same slope are parallel and never meet.
• Everyday rules such as “fixed charge + rate × quantity” are linear: fare = 30 + 12x.

Remember

Watch out

• Getting the sign of the zero wrong: the zero of 2x + 6 is −3, not 3.
• Mixing up the slope (the number with x) and the intercept (the constant).
• Thinking a line with a bigger intercept is steeper.

Worked example