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Understanding Rectangular Coordinates and Linear Equations in the Coordinate Plane

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maite-york
17 diapositives · 339 Views · Nov 13, 2014

This guide introduces the concept of rectangular coordinates, focusing on the parts of a coordinate plane and the significance of the X and Y axes. It explains the four quadrants and how to identify coordinates based on their position. Learn how positive and negative values define locations in each quadrant. The guide also covers how to graph points (e.g., (4,2), (4,-3), (-4,-3)) and find pairs of values that satisfy linear equations. Discover the relationship between coefficients and graphs to better understand linear equations.

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Understanding Rectangular Coordinates and Linear Equations in the Coordinate Plane
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  1. Rectangular Coordinates & Linear Equations

  2. Rectangular Coordinates • Parts of a coordinate plane • Y axis • Vertical line • X axis • Horizontal line • Quadrants • The 4 parts that the coordinate plane is divided into

  3. Quadrants • The upper right quadrant is the first quadrant and the rest go counterclockwise.

  4. Points in Quadrant 1 have positive x and positive y coordinates. • Points in Quadrant 2 have negative x but positive y coordinates. • Points in Quadrant 3 have negative x and negative y coordinates. • Points in Quadrant 4 have positive x but negative y coordinates.

  5. X and Y Coordinates • X-Coordinate • Tells how far the point is to the right or left of the y-axis • The first number in the set • Y-Coordinate • Tells how far above or below the x-axis • The second number in the set

  6. (x-coordinate, y-coordinate)

  7. Graph the following points: • (4, 2) • (4,-3) • (-4, -3)

  8. If we have an equation with one variable, then the solution is the one number that makes the equation true. • If we have an equation with two variables, then the solutions are the pairs of values that make the equation true.

  9. y = x + 2 Y= 5 and x = 3 would make this statement true along with y=6 and x=4, etc. There are many pairs that make this statement true. If we took those numbers and plotted them on a coordinate plane, they would form a straight line.

  10. When graphing a line, you should find at least three pairs of values. • Make a chart to keep up with which numbers go together.

  11. Example x y x y • y = x – 2 Fill in chart!

  12. Now, graph the points on a coordinate plane.

  13. Example x y Y = 2x + 1