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# Writing linear equations

## on Sep 21, 2010

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## Writing linear equationsPresentation Transcript

• Writing Linear Equations
• Using Slope Intercept Form
• Point-Slope Form.
•
• We’ve learned to graph given an equation.
• Now we’ll learn to write the equation given the graph
• There are three ways.
• It all depends on what information you are given as to which process you use.
• Slope-Intercept Form
• y = mx + b [or f ( x ) = mx + b ]
• m is the slope
• b is the y -intercept
• Find the Equation of the Line
• What is the
• y -intercept?
• b = -2
• What is m ?
• m =
• y = x -2
x y
• Find the Equation of the Line
• b = ?
• b = 1
• m = ?
• m = -
• y = - x + 1
x y
• Find the Equation of the Line
• b = ?
• b = 4
• m = ?
• m = 0
• y = 0 x + 4
• y =4
x y
• Find the Slope and y-intercept of each Equation:
• 1) y = -4 x + 3
• m = -4
• b = 3
• 2) y = 5 - x
• m = -
• b = 5
• 3) 8 x + y =
• m = -8
• b =
• 4) 4 x - 2 y = 10
• m = 2
• b = -5
• Find the Equation Given the Slope and y -intercept
• 1) m = -3, b = 1
• y = -3 x + 1
• 2) m = - , b = -4
• y = - x - 4
• Find the Equation Given the Slope and a Point
• Given m = -1, (2, 1)
• First, calculate b by substituting the slope and the coordinates into y = mx + b.
• y = -1 x + b
• 1 = -1(2) + b
• 1 = -2 + b
• 3 = b
• y = -1 x + 3
• If you are given two points on the line
• Find the slope using the two points
• Then plug this slope and either one of the points into the point slope formula.
• Find the Equation Given Two Points
• Given (-1, 3) and (2, 1)
• First, calculate the slope:
• Second, find b . Use either point...
• m = , (2, 1)
• 1 = (2) + b
• 1 = + b
• = b
• Use Point Slope Form: If you are given slope, m, and a point (x 1 ,y 1 ) on the line
• y – y 1 = m ( x – x 1 )
• Write an equation of a line containing the point (1,2) with slope of -1/2.
• Use (x 1 ,y 1 ) = (1,2) & m = -1/2
• y – 2 = -1/2 ( x – 1)
• Now you can simplify to the slope intercept form
• y – 2 = -1/2 x + ½
• y = -1/2 x + 5/2
• Given two points (-2,2) & (3,7)
• Find the slope:
• m=1
• Plug this slope and one of the points into the point slope formula.
• y – 2 = 1 ( x – (-2))
• y – 2 = x + 2
• y = x + 4 (put the equation into slope intercept form)
(-2,2) (3,7)