Introduction to Linear Polynomials
The y-intercept and parallel lines
Find out what the number b does to the line y = ax + b.
Where does the line cross the y-axis?
- y = 2x + 5 at A (0, 5);
- y = x + 3 at B (0, 3);
- y = 3x – 2 at C (0, –2).
Any line y = ax + b cuts the y-axis at (0, b), because x = 0 there. b is called the y-intercept. For y = 3x – 2 it is –2: the line crosses 2 units below the origin.
So in y = ax + b: a is the slope, b is the y-intercept.
Change a, keep b: the line turns about the point (0, b). y = 3x + 1 rises and y = –3x + 1 falls, through the same point (0, 1).
Change b, keep a: the line slides up or down but keeps its tilt, so the lines are parallel. y = 2x – 1, y = 2x + 1 and y = 2x + 5 are parallel. Equal slopes, different intercepts: parallel lines.
If the equation is not in the form y = ax + b, divide first: 2y = 4x + 7 becomes y = 2x + 3.5.
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