Lesson 3.8 Writing Linear Equations Given Two Points Objective- To write a linear equation given a point and a slope or given two points. 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 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

No fractional coefficients! Write a linear equation in standard form given: 1 slope = y-intercept = -2 4 y = mx + b 1 y = x - 2 Not in standard form! 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 fractional coefficients! 4 - x + 4y = -8 x - 4y = 8 or Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

-1 (x,y) y = mx + b -1 -1 y = x + y = x + b -1 4 = (2) + b -2 4 = + b Write a linear equation in standard form given: -1 slope = point = (2,4) 5 (x,y) y = mx + b -1 22 -1 y = x + y = x + b 5 5 5 1 1 -1 + x + x 4 = (2) + b 5 5 5 -2 4 = + b 1 22 5 x + y = 5 5 5 2 2 + + 5 5 x + 5y = 22 2 22 4 = b = 5 5 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

-11 -2 = (1) + b -2 = + b -11 -14 -11 -3 (x,y) y = mx + b -3 -3 Write a linear equation in standard form given: -3 slope = point = (1,-2) 7 (x,y) y = mx + b -3 -11 -3 y = x + y = x + b 7 7 7 3 3 -3 + x + x -2 = (1) + b 7 7 7 -3 -2 = + b -11 3 7 x + y = 7 7 7 3 3 + + 7 7 3x + 7y = -11 3 -2 + = b 7 -14 -11 3 + = b = 7 7 7 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

-12 - x - x -3 -12 - - -3x + 5y = -12 -12 -12 (x,y) y = mx + b (4,0) 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 - x - x 3 3 3 0 = (4) + b 5 5 5 12 -3 -12 0 = + b 5 x + y = 5 5 5 - - 12 12 5 5 -3x + 5y = -12 -12 -12 0 + = b = or 5 5 3x - 5y = 12 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Change in price = $0.80/ brick y = 0.80x + b m = 0.80 A masonry company charges $0.80 a brick. The company will charge $465 for 500 bricks to be delivered to a site. If x = the number of bricks, and y = total cost, write an equation for y in terms of x. Slope y = mx + b Change in price = $0.80/ brick y = 0.80x + b m = 0.80 465 = 0.8(500) + b 465 = 400 + b Point -400 -400 500 bricks cost $465 65 = b (x, y) = (500, 465) y = 0.8x + 65 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

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 y 3 Slope (m) = = x x2- x1 4 15 4 b = 5 - - = 5 - 3 3 3 3 2 Slope (m) = = 4 - -2 11 6 b = 1 11 1 3 y = x + m = 3 3 3 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

the line which contains: Write the equation of the line which contains: (0, -3) (4, 8) y = mx + b (x, y) 11 y = x + b y2- y1 4 y Slope (m) = = x x2- x1 11 8 = (4) + b 4 8 - -3 11 Slope (m) = = 4 - 0 8 = 11 + b 4 11 b = 8 - 11 = -3 m = 4 b = -3 11 y = x - 3 4 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

-3.95 -3.95 Suppose a 5 minute call costs $6.20 and a 20 minute call costs $18.05. Write an equation which describes cost y in terms of x minutes. (minutes, cost) (x, y) (5, 6.20) (20, 18.05) y = mx + b y2- y1 18.05 - 6.20 y = 0.79x + b m = = x2- x1 20 - 5 6.20 = 0.79(5) + b 11.85 m = = 0.79 6.20 = 3.95 + b 15 -3.95 -3.95 2.25 = b y = 0.79x + 2.25 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

-12 -12 Use the x-y chart below to write a linear equation that satisfies all the points. x y 2 4 4 10 7 19 9 25 14 40 y = mx + b +2 +6 y = 3x + b +3 +9 10 = 3(4) + b +2 +6 +5 +15 10 = 12 + b -12 -12 y2- y1 10 - 4 -2 = b m = = x2- x1 4 - 2 6 m = = 3 y = 3x - 2 2 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series