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Objective- To write a linear equation given a point and a slope.

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 = mx + b. y = 3x + - 2. Not in standard form!. - 3x - 3x. Ax + By = C.

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Objective- To write a linear equation given a point and a slope.

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  1. 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 = mx + b y = 3x +-2 Not in standard form! -3x -3x Ax + By = C -3x + y =-2 Where A, B and C are integers. or 3x - y = 2

  2. Write a linear equation in standard form given: 1 slope = y-intercept =-2 4 y = mx + b 1 Not in standard form! y = x - 2 4 Ax + By = C 1 1 - x - x 4 4 Where A, B and C are integers. 1 - x + y =-2 4 1 4 - x + y =-2 No fractions! 4 x - 4y = 8 - x + 4y =-8 or

  3. 1 1 + x + x 5 5 2 2 ++ 5 5 Write a linear equation in standard form given: -1 slope = point =(2,4) 5 (x,y) y = mx + b -1 22 y = x + -1 y = x + b 5 5 5 -1 4 = (2) + b 5 -2 22 4 =+ b 1 5 x + y = 5 5 5 x + 5y = 22 2 22 4 = b = 5 5

  4. 3 3 + x + x 7 7 3 3 ++ 7 7 Write a linear equation in standard form given: -3 slope = point =(1,-2) 7 (x,y) y = mx + b -11 -3 y = x + -3 y = x + b 7 7 7 -3 -2 = (1) + b 7 -3 -11 -2 =+ b 3 7 x + y = 7 7 7 3x + 7y = -11 3 -2 + = b 7 -14 -11 3 = + = b 7 7 7

  5. 3 3 - x - x 5 5 -- 12 12 5 5 Write a linear equation in standard form given: 3 slope = x-intercept = 4 5 (x,y) y = mx + b (4,0) -12 3 y = x + 3 y = x + b 5 5 5 3 0 = (4) + b 5 -12 12 -3 0 =+ b 5 x + y = 5 5 5 -3x + 5y = -12 -12 = b or 5 3x - 5y = 12

  6. Finding an Equation Given Two Points y = mx + b 1 Write the equation of the line which contains: y = x + b 3 1 5 = (4) + b (-2, 3) (4, 5) 3 (x, y) 4 y2- y1 5 =+ b 3 Slope (m) = x2- x1 4 15 4 b = 5 - - = 5 - 3 3 3 3 2 Slope (m) = = 11 4 - -2 6 b = 3 1 11 1 y = x + m = 3 3 3

  7. Write the equation of the line which contains: (0, -3) (4, 8) y = mx + b (x, y) 11 y = x + b y2- y1 4 Slope (m) = x2- x1 11 8 = (4) + b 4 8 - -3 11 Slope (m) = = 4 - 0 8 = 11 + b 4 -11 -11 11 m = -3 = b 4 b = -3 11 y = x -3 4

  8. Use the x-y chart below to write a linear equation that satisfies all the points. x y y = mx + b 2 4 4 10 7 19 9 25 14 40 +6 +2 y = 3x + b +3 +9 10 = 3(4) + b +6 +2 10 = 12 + b +5 +15 -12 -12 y2- y1 10 - 4 -2 = b m = = x2- x1 4 - 2 6 3 y = 3x - 2 m = = 2

  9. The graph below represents the volume of water in a tank (y) over time (x). Find the equation that describes y in terms of x. 60 50 40 30 20 10 0 Water Level (Gal.) 0 1 2 3 4 5 Hours

  10. The graph below represents the total cost of a taxi ride (C) over miles driven (n). Find the equation that describes C in terms of n. C 60 50 40 30 20 10 0 Total Cost 0 5 10 15 20 25 n Miles

  11. Point-Slope Form Write the equation of a line in point-slope form that passes through (2,5) with a slope of -3.

  12. Forms of the Linear Equation Standard Form Slope-Intercept Form Point-Slope Form

  13. Write the equation in slope-intercept form that passes through (-2,6) with slope of 3.

  14. Write the equation in slope-intercept form that passes through (5,-1) with slope of .

  15. Write the equation of the line below in slope-intercept form. y -2 +3 x (-2, 3)

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