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Introduction to Coordinate Plane Graphing: Understanding Functions and Equations

Learn the fundamentals of graphing on a coordinate plane, including coordinates, quadrants, variables, and equations with ordered pairs. Discover how to identify independent and dependent variables in various scenarios and solve equations with multiple solutions. Get ready for a test with warm-up exercises and homework assignments.

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Introduction to Coordinate Plane Graphing: Understanding Functions and Equations

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  1. Warm Up • The distance from a number to 0 on the number line is the ___________________________.

  2. Lesson 20, Graphing on a Coordinate Plane Expressions and equations, Functions

  3. Vocabulary • Coordinate plane: two perpendicular axes; one horizontal, one vertical • X-axis: the horizontal axis • Y-axis: the vertical axis • Origin: intersection of the x-axis and y-axis • Ordered pair: identifies a point on the coordinate plane • X-coordinate: indicates horizontal distance • Y-coordinate: indicates vertical distance

  4. Coordinate Plane • The coordinate plane has four quadrants. • The first quadrant contains all positive values • The second quadrant contains negative x values and positive y values • The third quadrant contains all negative values • The fourth quadrant contains positive x values and negative y values

  5. Example Graph the point Graph the point

  6. Variables • Independent variable: the variable whose value can be chosen • Dependent variable: the variable whose value is determined by the value of another variable

  7. Example For each pair of variables, identify the independent variable and dependent variable. • Number of traffic violations, cost of auto insurance • Electric bill total, kilowatts of electricity used

  8. Equations and ordered pairs • A solution to an equation with two variables is an ordered pair that makes the equation true. • The equation has infinitely many solutions. • We can find solutions by substituting values for to find the corresponding values.

  9. Example The federal minimum wage is about $5 per hour. The total on a minimum-wage worker’s paycheck is dependent on the number of hours worked. The paycheck total can be calculated using the equation . Find the pay for 1, 3, 5, and 8 hours of work. Graph the solution.

  10. Correcting homework • Be kind • Write “C.B. _____________” with your name • Hold questions until the end • Make sure I get your score sheet so your assignment is not marked missing!

  11. Homework • 1st and 2nd hour: Lesson 20 #1-30 • 3rd hour: Lesson 19 #16-30 • Test tomorrow! Don’t forget to study!

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