The Cartesian Plane, Linear Graphs, and Gradient

Comprehensive vocabulary flashcards covering the key terms, components, definitions, and formulas related to the Cartesian plane, linear graphs, and gradients.

$x$-axis

The horizontal number line on the Cartesian or number plane.

$y$-axis

The vertical number line on the Cartesian or number plane.

Origin

The central point on a number plane where the horizontal $x$-axis and the vertical $y$-axis intersect.

Independent variable

The variable (commonly $x$) whose values can be freely chosen or set to determine the outcome of a relation.

Dependent variable

The variable (commonly $y$) whose values are determined by and depend on the values of the independent variable.

Equation of a line

An equation that connects the $x$ and $y$-coordinates of all points located on that straight line.

Gradient (or Slope)

The comparison of the vertical step to the horizontal step, calculated as: $\text{gradient} = \frac{\text{vertical step}}{\text{horizontal step}}$.

Gradient of a horizontal line

A gradient equal to $0$ because the vertical step is $0$, which produces $0$ as the numerator.

Gradient of a vertical line

A gradient that is undefined because the horizontal step is $0$, which produces $0$ in the denominator.

Two-point gradient formula

The formula used to determine the gradient of a line passing through points $A(x_1, y_1)$ and $B(x_2, y_2)$: $\frac{y_2 - y_1}{x_2 - x_1}$.

$x$-intercept

The point where a straight line meets or crosses the $x$-axis.

$y$-intercept

The point where a straight line meets or crosses the $y$-axis.

$$y = mx + c$$

The gradient-intercept form for the equation of a straight line, where $m$ is the gradient and $c$ is the $y$-intercept.