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AA 3.4

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AA 3.4 AA 3.4 Presentation Transcript

  • Warm Up How are the two graphs similar? and different? 3x + 4y = 24 and y = 3x + 6
  • 3.4 The Graph of Ax + By = C E. Q. - How do we graph linear graphs from standard form by determining the slope and y-int?
  • VOCABULARY
  • VOCABULARY standard form - for a linear function, Ax+By = C
  • VOCABULARY standard form - for a linear function, Ax+By = C Oblique lines - lines with slopes that are not zero or undefined
  • VOCABULARY standard form - for a linear function, Ax+By = C Oblique lines - lines with slopes that are not zero or undefined zero slope lines - lines of the form y = #
  • VOCABULARY standard form - for a linear function, Ax+By = C Oblique lines - lines with slopes that are not zero or undefined zero slope lines - lines of the form y = # Undefined slope lines - lines of the form x = #
  • VOCABULARY standard form - for a linear function, Ax+By = C Oblique lines - lines with slopes that are not zero or undefined zero slope lines - lines of the form y = # Undefined slope lines - lines of the form x = # x-intercept - where the graph crosses the x- axis
  • VOCABULARY standard form - for a linear function, Ax+By = C Oblique lines - lines with slopes that are not zero or undefined zero slope lines - lines of the form y = # Undefined slope lines - lines of the form x = # x-intercept - where the graph crosses the x- axis y-intercept - where the graph crosses the y-axis
  • Theorem: the graph of Ax + By = C, where A and B are both not zero, is a line.
  • Examples Tell whether each line is oblique, vertical or horizontal and then state the slope.
  • Examples Tell whether each line is oblique, vertical or horizontal and then state the slope. 1. y = 4 x + 4 3 €
  • Examples Tell whether each line is oblique, vertical or horizontal and then state the slope. 1. y = 4 x + 4 3 2. y = −8x − 9 € €
  • Examples Tell whether each line is oblique, vertical or horizontal and then state the slope. 1. y = 4 x + 4 3 2. y = −8x − 9 € € 3. x = 7 €
  • Examples Tell whether each line is oblique, vertical or horizontal and then state the slope. 1. y = 4 x + 4 3 2. y = −8x − 9 € € 3. x = 7 4. y = −2 € €
  • Examples Tell whether each line is oblique, vertical or horizontal and then state the slope. 1. y = 4 x + 4 3 2. y = −8x − 9 oblique slope = 3/4 € € 3. x = 7 4. y = −2 € €
  • Examples Tell whether each line is oblique, vertical or horizontal and then state the slope. 1. y = 4 x + 4 3 2. y = −8x − 9 oblique oblique slope = 3/4 slope = -8 € € 3. x = 7 4. y = −2 € €
  • Examples Tell whether each line is oblique, vertical or horizontal and then state the slope. 1. y = 4 x + 4 3 2. y = −8x − 9 oblique oblique slope = 3/4 slope = -8 € € 3. x = 7 4. y = −2 vertical slope = undefined € €
  • Examples Tell whether each line is oblique, vertical or horizontal and then state the slope. 1. y = 4 x + 4 3 2. y = −8x − 9 oblique oblique slope = 3/4 slope = -8 € € 3. x = 7 4. y = −2 vertical horizontal slope = undefined slope = 0 € €
  • Graphing Using Intercepts 5. Graph 10x + 6y = 30 using the intercepts.
  • Graphing Using Intercepts 5. Graph 10x + 6y = 30 using the intercepts. To find the x-intercept, plug in 0 for y and solve.
  • Graphing Using Intercepts 5. Graph 10x + 6y = 30 using the intercepts. To find the x-intercept, plug in 0 for y and solve. 10x + 6(0) = 30
  • Graphing Using Intercepts 5. Graph 10x + 6y = 30 using the intercepts. To find the x-intercept, plug in 0 for y and solve. 10x + 6(0) = 30 10x = 30
  • Graphing Using Intercepts 5. Graph 10x + 6y = 30 using the intercepts. To find the x-intercept, plug in 0 for y and solve. 10x + 6(0) = 30 10x = 30 x=3
  • Graphing Using Intercepts 5. Graph 10x + 6y = 30 using the intercepts. To find the x-intercept, To find the y-intercept, plug in 0 for y and solve. plug in 0 for x and solve. 10x + 6(0) = 30 10x = 30 x=3
  • Graphing Using Intercepts 5. Graph 10x + 6y = 30 using the intercepts. To find the x-intercept, To find the y-intercept, plug in 0 for y and solve. plug in 0 for x and solve. 10x + 6(0) = 30 10(0) + 6y = 30 10x = 30 x=3
  • Graphing Using Intercepts 5. Graph 10x + 6y = 30 using the intercepts. To find the x-intercept, To find the y-intercept, plug in 0 for y and solve. plug in 0 for x and solve. 10x + 6(0) = 30 10(0) + 6y = 30 10x = 30 6y = 30 x=3
  • Graphing Using Intercepts 5. Graph 10x + 6y = 30 using the intercepts. To find the x-intercept, To find the y-intercept, plug in 0 for y and solve. plug in 0 for x and solve. 10x + 6(0) = 30 10(0) + 6y = 30 10x = 30 6y = 30 x=3 y=5
  • Graphing Using Intercepts 5. Graph 10x + 6y = 30 using the intercepts. To find the x-intercept, To find the y-intercept, plug in 0 for y and solve. plug in 0 for x and solve. 10x + 6(0) = 30 10(0) + 6y = 30 10x = 30 6y = 30 x=3 y=5 Now plot the points and draw the line.
  • 6. Graph 7y = -21
  • 6. Graph 7y = -21 y = -21/7
  • 6. Graph 7y = -21 y = -21/7 y = -3
  • 6. Graph 7y = -21 y = -21/7 y = -3 So is it a vertical or horizontal line?
  • 6. Graph 7y = -21 y = -21/7 y = -3 So is it a vertical or horizontal line?
  • 7. Give the equation in standard form of the line with slope -3/4 and y-int of 5.
  • 7. Give the equation in standard form of the line with slope -3/4 and y-int of 5. y= -3/4x + 5
  • 7. Give the equation in standard form of the line with slope -3/4 and y-int of 5. y= -3/4x + 5 Add 3/4x to both sides.
  • 7. Give the equation in standard form of the line with slope -3/4 and y-int of 5. y= -3/4x + 5 Add 3/4x to both sides. 3/4x + y = 5
  • 7. Give the equation in standard form of the line with slope -3/4 and y-int of 5. y= -3/4x + 5 Add 3/4x to both sides. 3/4x + y = 5 Multiply everything by 4.
  • 7. Give the equation in standard form of the line with slope -3/4 and y-int of 5. y= -3/4x + 5 Add 3/4x to both sides. 3/4x + y = 5 Multiply everything by 4. 3x + 4y = 20
  • Why do we need standard form?
  • Why do we need standard form? slope-intercept can only give horizontal and oblique lines.
  • Why do we need standard form? slope-intercept can only give horizontal and oblique lines. standard form can give any line in the coordinate plane
  • Summary: What is the standard form of an equation? What is the slope-intercept form of an equation?
  • Summary: What is the standard form of an equation? Ax + By = C where A, B, and C are numbers What is the slope-intercept form of an equation?
  • Summary: What is the standard form of an equation? Ax + By = C where A, B, and C are numbers What is the slope-intercept form of an equation? y = mx + b where m and b are numbers
  • Homework page 160, 161 6 - 26