14 Questions
In which quadrant does the point (-1.5, -2.5) lie?
Quadrant III
What are the coordinates of the point where the line y = 2x crosses the y-axis?
(0, 4)
What is the slope of the line passing through the points (-4, -3) and (4, -1)?
1/4
If a point lies on the y-axis, what can you say about its x-coordinate?
It is always zero
What type of correlation does the equation y = -3x - 2 represent?
Negative correlation
For which line do both the x- and y-coordinates have the same sign?
y = 2x
Which quadrant will a line be in if it has a positive slope and both x-intercept and y-intercept are positive?
Quadrant I
In which quadrant do the cartesian coordinates (-2, 4) lie?
Quadrant II
What type of correlation does the equation y = 1/4x - 2 represent?
Positive correlation
If a point lies on the x-axis, what can you say about its y-coordinate?
It is always zero
Which line does NOT pass through the origin?
y = 1/4x - 2
What is the slope of the line passing through the points (-4, -3) and (4, -1)?
-1/4
If a line has a negative slope and a positive y-intercept, which quadrant will it be in?
Quadrant III
In which quadrant do the cartesian coordinates (-4, -1) lie?
Quadrant I
Study Notes
Introduction to Cartesian Coordinate System
- The Cartesian Coordinate System is a method of locating points in space using an origin, x- and y-axes, and a unit length.
- According to legend, French mathematician Rene Descartes developed the system while observing a fly on the ceiling.
Cartesian Graph
- A Cartesian graph is composed of a horizontal line (x-axis) and a vertical line (y-axis) that intersect at the origin.
- The axes can be divided and numbered using any unit of measurement.
- Points are located on the graph using ordered pairs, where the first number is the x-coordinate and the second number is the y-coordinate.
Locating Points
- The x-coordinate indicates the distance from the y-axis along the x-axis, and the y-coordinate indicates the distance from the x-axis along the y-axis.
- Points can be located in one of four quadrants: I (above x-axis and to the right of y-axis), II (above x-axis and to the left of y-axis), III (below x-axis and to the left of y-axis), and IV (below x-axis and to the right of y-axis).
- Quadrant I has positive x- and y-coordinates, Quadrant II has negative x-coordinates and positive y-coordinates, Quadrant III has negative x- and y-coordinates, and Quadrant IV has positive x-coordinates and negative y-coordinates.
Three or More Dimensions
- The Cartesian Coordinate System can be extended to three dimensions by adding a z-axis, which begins at the origin and extends in positive and negative directions perpendicular to the coordinate plane.
- The z-axis allows for the indication of height or depth of a 3-dimensional figure.
Graphing Lines
- Lines can be graphed using Cartesian coordinates and equations, such as y = 2x, y = -3x -2, and y = 1/4x -2.
- Points on the graph can be located and connected to form a straight line.
Learn about the Cartesian Coordinate System, which was developed by French mathematician Rene Descartes in the 17th century. This system uses a set of coordinates, an origin point, and axes to locate objects in a two-dimensional space.
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