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Graphing Linear Equations

Graphing Linear Equations. Graphing Linear Equations. Linear equation: an equation with two variables that are both to the first power . Ex. x + y = 3 The graph of a linear equation will always be a straight line.

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Graphing Linear Equations

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  1. Graphing Linear Equations

  2. Graphing Linear Equations • Linear equation: an equation with two variables that are both to the first power. Ex. x + y = 3 • The graph of a linear equation will always be a straight line.

  3. Previously, you’ve solved equations that contain just one variable. For example, let’s solve: 2x + 3 = 7

  4. Linear equations have an infinite number of solutions. • When we solve a linear equation, we get a list of ordered pairs. • The graph of all of the ordered pairs creates a straight line.

  5. x + y = 3

  6. Ordered Pairs

  7. Horizontal and Vertical Lines • Sometimes, the graph of an equation is a horizontal or a vertical line. • If our equation only contains a “y”, then our graph is a horizontal line. • If our equation only contains an “x”, then our graph is a vertical line.

  8. Example y = 3

  9. Example x = 3

  10. Examples For each of the following linear equations: • Find four ordered pair that complete the equation • Plot the ordered pairs on a coordinate plane • x + y = 6 2) y = x + 1 3) x = 4

  11. x + y = 6 Ordered Pairs

  12. Y = x + 1 Ordered Pairs

  13. x = 2 Ordered Pairs

  14. Slope • Slope: A number which is used to indicate the steepness of a line, as well as indicating whether the line is tilted uphill or downhill. • Think of a road going uphill (or downhill). The steepness of the road is the slope.

  15. The slope we are studying is associated with the graph of a line.

  16. Steepness

  17. Vertical ChangeHorizontal Change This ratio is also known as Rise Run

  18. Graph (3,2) and (-1,-1)

  19. Draw a line through the points.

  20. Now that we have our line lets find its slope. Remember we are finding the following ratio: Vertical or Rise Horizontal Run

  21. Vertical Changeor the Rise 3

  22. Horizontal Changeor the Run 4 3

  23. Vertical RiseHorizontal Run 3 4

  24. Find the slope of the following line.

  25. The slope is… 1 2

  26. Find the slope of the line.

  27. The slope is…. -3

  28. Find the slope of these lines.

  29. The slope is… • Black line 3 • Red Line 1 • Blue Line -1/2

  30. Find the slope of these lines

  31. The slope is… • Orange line 0 • Green Line Undefined

  32. Let’s go back to our first example. • Graph the line that goes through (3,2) and (-1,-1)

  33. Equation (3,2) and (-1,-1)

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