5.3 Standard Form of a Line. 3 3 3 1 33 Finding an Equation Given Two Points Write the equation of the line which contains: (-2, 3) (4, 5) Slope (m)=

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Presentation transcript:

5.3 Standard Form of a Line

Finding an Equation Given Two Points Write the equation of the line which contains: (-2, 3) (4, 5) Slope (m)= y 2 - y 1 x 2 - x 1 y = mx + b Slope (m) = = 2 6 m = 1 3 y = x + b (x, y) 5 = (4) + b 1 5 = + b 4 b = = b = 11 3 y = x + 111

4 4 4 Write the equation of the line which contains: (0, - 3) (4, 8) Slope (m)= y 2 - y 1 x 2 - x 1 y = mx + b Slope (m) = = 11 4 m = 11 4 y = x + b (x, y) 8 = (4) + b 8 = 11 + b = b b = - 3 y = x

Objective- To graph and manipulate equations in standard form. Standard FormSlope-Intercept Form Ax + By = C y = mx + b 3x + 2y = 8 - 3x 2y = - 3x y = x y = x m = b = 4 To change Standard Form to Slope-Intercept Form just solve the equation for y.

Graph the following equation. - 4x + 3y = 6 +4x 3y = 4x y = x y = x m = 4 3 b = 2 x y

Graph the following equation. y = x m = 1 b = 0 x y y = 1x + 0

Convert the following linear equation to standard form. Not in standard form ! Ax + By = C y = 2x x -2x + y = 5 or2x - y = -5

- x + y = 4 - x Write a linear equation in standard form given: slope = y-intercept = y = mx + b y = x Not in standard form ! Ax + By = C Where A, B and C are integers No fractional coefficients! 3 - 2x + 3y = 12 or 2x - 3y = - 12

- x + y = -1 - x Write a linear equation in standard form given: slope = y-intercept = y = mx + b y = x Not in standard form ! Ax + By = C Where A, B and C are integers No fractional coefficients! 4 - 5x + 4y = -4 or 5x - 4y = 4

Objective- To write a linear equation given a point and a slope. Write a linear equation in standard form given: slope = 3 y-intercept = - 2 m = 3 b = - 2 y = 3x y = mx + b Not in standard form! Ax + By = C - 3x - 3x + y = - 2 Where A, B and C are integers. or 3x - y = 2

- x + y = -2 - x Write a linear equation in standard form given: slope = y-intercept = y = mx + b y = x Not in standard form ! Ax + By = C Where A, B and C are integers No fractions! 4 - x + 4y = -8 or x - 4y = 8

5 x + y = 5 + x Write a linear equation in standard form given: slope = point = (2,4) -1 5 y = mx + b y = x + b -1 5 (x,y) 4 = (2) + b = + b = b 2 5 = 22 y = x x + 5y = 22