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

y = mx + b y = x - 2 Not in standard form! Ax + By = C - x - x 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 fractions! 4 - x + 4y = -8 x - 4y = 8 or

-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 5 + x + x 1 -1 4 = (2) + b 5 -2 4 = + b 1 22 5 x + y = 5 5 5 5 + + 2 x + 5y = 22 2 22 4 = b = 5 5

-11 -2 = (1) + b -11 -2 = + b -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 + x + x 3 7 -3 -2 = (1) + b 7 -3 -2 = + b -11 3 7 x + y = 7 7 7 + + 3 7 3x + 7y = -11 3 -2 + = b 7 -14 -11 3 + = b = 7 7 7

-12 - x - x -3 -12 - - -3x + 5y = -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 5 3 0 = (4) + b 5 12 -3 -12 0 = + b 5 x + y = 5 5 5 - - 5 12 -3x + 5y = -12 -12 = b or 5 3x - 5y = 12

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) = = 4 - -2 11 6 b = 3 1 11 1 y = x + m = 3 3 3

-3 = b Write the equation of the line which contains: (0, -3) (4, 8) (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

-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

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 Water Level (Gal.) 0 1 2 3 4 5 Hours

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 Total Cost 0 5 10 15 20 25 n Miles

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

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

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

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

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