Graphs Terms

Gradient (m)

The measure of the steepness of a line, calculated as Change in y / Change in x (Rise / Run).

y-intercept (c)

The point where a line crosses the y-axis (where x = 0).

x-intercept

The point where a graph crosses the x-axis (where y = 0).

Linear Equation

An equation in the form y = mx + c that produces a straight line when plotted on a graph.

Parabola

The smooth U-shaped or n-shaped curve formed by a quadratic graph (y = ax^2 + bx + c).

Parallel Lines

Lines running in the exact same direction that never meet, characterized by having identical gradients.

Perpendicular Lines

Lines that intersect at a 90-degree angle, whose gradients are negative reciprocals of each other (m1 * m2 = -1).

Point of Intersection

The coordinate (x, y) where two or more lines cross, representing the solution to simultaneous equations.

Roots of a Graph

The x-values where a curve crosses or touches the x-axis (where y = 0).

Step Graph

A graph composed of disconnected horizontal line segments representing values that jump abruptly at specific thresholds.

Exponential Growth

A curve (y = a^x) that starts shallow near the x-axis and grows rapidly steeper as x increases.

Cover-Up Method

A shortcut method used to quickly find x- and y-intercepts to plot equations in the form ay + bx = c.

Open (◦) vs Closed Circle (•)

A closed circle (•) means the endpoint value is INCLUDED, while an open circle (◦) means the endpoint value is EXCLUDED.