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Line and its slope

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1. The document discusses various forms of linear equations including standard form (Ax + By = C), slope-intercept form (y = mx + b), and point-slope form (y - y1 = m(x - x1)). 2. It provides examples of transforming linear functions between these forms and discusses how to find the slope and y-intercept of a linear function from its graph. 3. The slope and direction of a linear function's graph is determined by whether its slope is positive or negative. A positive slope produces an upward rising line while a negative slope produces a downward falling line.

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Line & Its Slope

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STANDARD FORM OF LINEAR EQUATION Ax + By = C Transform each linear function in standard form. 1. y = -9x + 2 9x + y = 2 2. y = 3/2 – 2x 2 (y = 3/2 – 2x) 2 2y = 3 – 4x 4x + 3y = 3

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STANDARD FORM OF LINEAR EQUATION Ax + By = C 3. 𝟐𝒙 𝟑 - 𝒚 𝟒 = 1 4. y - 𝟏 𝟐 = 2(x + 1) 12 ( 𝟐𝒙 𝟑 - 𝒚 𝟒 = 1) 12 8x - 3y = 12 y - 𝟏 𝟐 = 2x + 2 2 (y - 𝟏 𝟐 = 2x + 2) 2 2y - 𝟏= 4x + 4 -4x + 2y = 4+1 -1(-4x + 2y = 5)-1 4x - 2y = -5

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SLOPE – INTERCEPT FORM y = mx + b Transform each linear function in slope intercept form. Then, identify the value of m and b. 1. 4x - y = 1 2. 2x + 3y = 6 3. 𝟑 𝟐 x + 𝟏 𝟑 y + 1 = 0 4. 𝒙 𝟐 + 𝒚 𝟓 = 3

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Linear Equation Graph each linear function. 1. y = 3x - 2 X -1 0 2 y

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SLOPE OF A LINE If 𝑷 𝟏 𝒙 𝟏, 𝒚 𝟏 𝒂𝒏𝒅𝑷 𝟐 𝒙 𝟐, 𝒚 𝟐 are points of the line representing the linear function y = mx + b, then the slope m of the line is m = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 = 𝒚 𝟏−𝒚 𝟐 𝒙 𝟏−𝒙 𝟐

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SLOPE OF A LINE Determine the slope of the linear functions that passes through the given pairs of points. Then draw the graph of the linear functions. 1. (3,2) , (5,6) 2. (-2,0) , (1,-2)

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The Slope, the trends and the graph of linear function If the slope is positive, the graph of a linear function points upward to the right, and the linear function increases all throughout.

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The Slope, the trends and the graph of linear function If the slope is negative, the graph of a linear function points upward to the left, and the linear function decreases all throughout.

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The Point – Slope Form If the graph of a linear function y has a slope and passes through 𝒙 𝟏, 𝒚 𝟏 , then its equation is 𝒚 − 𝒚 𝟏 = m(𝒙 − 𝒙 𝟏)

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The Point – Slope Form Write the equation of the linear function y in slope- intercept form and in standard form whose graph passes through the given point and has given slope m. 1. (-1,2) , m = 2 2. (3,-2) , m = - 𝟑 𝟐

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The Two - Point Form If the graph of a linear function passes through the points 𝒙 𝟏, 𝒚 𝟏 and 𝒙 𝟐, 𝒚 𝟐 , then its equation is 𝒚 − 𝒚 𝟏 = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 (𝒙 − 𝒙 𝟏)

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Write the equation of the linear function y in slope- intercept form and in standard form whose graph passes through the given pairs of points. 1. (5,-4) , (-3,0) 2. (-4,3) , (5,-2) The Two - Point Form

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The Intercept Form If the graph of a linear function has x-intercept a and y- intercept b , then its equation is 𝒙 𝒂 − 𝒚 𝒃 = 𝟏

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Write the equation of the linear function y in slope- intercept form and in standard form whose graph has given x-intercept a and y-intercept b. 1. a = 2 , b = -3 2. a = −𝟏 𝟐 , 𝒃 = −𝟐 𝟑 The Two - Point Form

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Line and its slope

  • 1. Line & Its Slope
  • 2. STANDARD FORM OF LINEAR EQUATION Ax + By = C Transform each linear function in standard form. 1. y = -9x + 2 9x + y = 2 2. y = 3/2 – 2x 2 (y = 3/2 – 2x) 2 2y = 3 – 4x 4x + 3y = 3
  • 3. STANDARD FORM OF LINEAR EQUATION Ax + By = C 3. 𝟐𝒙 𝟑 - 𝒚 𝟒 = 1 4. y - 𝟏 𝟐 = 2(x + 1) 12 ( 𝟐𝒙 𝟑 - 𝒚 𝟒 = 1) 12 8x - 3y = 12 y - 𝟏 𝟐 = 2x + 2 2 (y - 𝟏 𝟐 = 2x + 2) 2 2y - 𝟏= 4x + 4 -4x + 2y = 4+1 -1(-4x + 2y = 5)-1 4x - 2y = -5
  • 4. SLOPE – INTERCEPT FORM y = mx + b Transform each linear function in slope intercept form. Then, identify the value of m and b. 1. 4x - y = 1 2. 2x + 3y = 6 3. 𝟑 𝟐 x + 𝟏 𝟑 y + 1 = 0 4. 𝒙 𝟐 + 𝒚 𝟓 = 3
  • 5. Linear Equation Graph each linear function. 1. y = 3x - 2 X -1 0 2 y
  • 6. SLOPE OF A LINE If 𝑷 𝟏 𝒙 𝟏, 𝒚 𝟏 𝒂𝒏𝒅𝑷 𝟐 𝒙 𝟐, 𝒚 𝟐 are points of the line representing the linear function y = mx + b, then the slope m of the line is m = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 = 𝒚 𝟏−𝒚 𝟐 𝒙 𝟏−𝒙 𝟐
  • 7. SLOPE OF A LINE Determine the slope of the linear functions that passes through the given pairs of points. Then draw the graph of the linear functions. 1. (3,2) , (5,6) 2. (-2,0) , (1,-2)
  • 8. The Slope, the trends and the graph of linear function If the slope is positive, the graph of a linear function points upward to the right, and the linear function increases all throughout.
  • 9. The Slope, the trends and the graph of linear function If the slope is negative, the graph of a linear function points upward to the left, and the linear function decreases all throughout.
  • 10. The Point – Slope Form If the graph of a linear function y has a slope and passes through 𝒙 𝟏, 𝒚 𝟏 , then its equation is 𝒚 − 𝒚 𝟏 = m(𝒙 − 𝒙 𝟏)
  • 11. The Point – Slope Form Write the equation of the linear function y in slope- intercept form and in standard form whose graph passes through the given point and has given slope m. 1. (-1,2) , m = 2 2. (3,-2) , m = - 𝟑 𝟐
  • 12. The Two - Point Form If the graph of a linear function passes through the points 𝒙 𝟏, 𝒚 𝟏 and 𝒙 𝟐, 𝒚 𝟐 , then its equation is 𝒚 − 𝒚 𝟏 = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 (𝒙 − 𝒙 𝟏)
  • 13. Write the equation of the linear function y in slope- intercept form and in standard form whose graph passes through the given pairs of points. 1. (5,-4) , (-3,0) 2. (-4,3) , (5,-2) The Two - Point Form
  • 14. The Intercept Form If the graph of a linear function has x-intercept a and y- intercept b , then its equation is 𝒙 𝒂 − 𝒚 𝒃 = 𝟏
  • 15. Write the equation of the linear function y in slope- intercept form and in standard form whose graph has given x-intercept a and y-intercept b. 1. a = 2 , b = -3 2. a = −𝟏 𝟐 , 𝒃 = −𝟐 𝟑 The Two - Point Form