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Graphing Equations

Cartesian Graph = Coordinate Plane

A Cartesian graph is a type of graph that helps us show the relationship between numbers using two lines, called axes.

The horizontal line is called the x-axis.
The vertical line is called the y-axis.

These lines meet at a point called the origin (0, 0).

The graph is divided into four sections, and we can plot points on it using pairs of numbers, like (x, y). Each point shows how far to go left or right on the x-axis, and up or down on the y-axis.

It’s a useful tool for showing patterns, relationships, and shapes in math!

This is a cartesian graph or coordinate plane.

Axes

Axes: The horizontal axis is the x-axis, and the vertical axis is the y-axis.

Quadrants

Quadrants: The plane is divided into four quadrants by the x and y axes.

Plotting Points

Points are plotted as ordered pairs (x, y).

A “coordinate point” is a specific spot on a graph, shown by a pair of numbers (x, y).

The “x” number tells you how far to move along the horizontal line (x-axis), and the “y” number tells you how far to move along the vertical line (y-axis).

It’s a way to find an exact location on the graph using these two numbers.

Graph of a line

A straight line is linear. It extends infinitely in both directions on the coordinate plane.

Fun fact: Any two points determine a unique line.

The equation of this line is: y = -2x + 2.

Intercepts

In algebra, an intercept is where a line crosses either the x-axis or y-axis on a graph.

X-intercept: This is where the line touches the x-axis (the horizontal line). At this point, the y-value is always zero. For the above graph, the x-intercept is (1, 0).

Y-intercept: This is where the line touches the y-axis (the vertical line). At this point, the x-value is always zero.For the above graph, the y-intercept is (0, 2).

Intercepts show where a line meets the axes on a graph.

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