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Equation Of A Line

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Section 1, Here\'s the powerpoint for math

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Equation Of A LinePresentation Transcript

• Equation of a Line
• 1. Slope and y -intercept
• 2. Graph
• 3. Slope and one point
• 4. Two points
• 5 . x - and y -intercepts
• Find the Equation of the Line Given the Slope and y -intercept
• m = -3, b = 1
• m = -2, b = -4
• m = 0, b = 10
• m = 1, b = 0
• m = 0, b = 0
• Substitute m and b into y = mx + b
y = -3 x + 1 y = -2 x - 4 y = 0 x + 10, y = 10 y = 1 x + 0, y = x y = 0 x + 0, y = 0
• Find the Equation of a Line Given the Graph
• Find the y -intercept from the graph.
• Count the slope from the graph.
• Example 1
• b = -3
• m =
• y = x - 3
x y
• Example 2
• b = 1
• m =
• y = x + 1
x y +1 -2
• Example 3
• b = 4
• m = 0/1= 0
• y = 0 x + 4, y = 4
x y
• Example 4
• x = 2
x y
• Dude! You try one.
• y = x + 2 x y
• Find the Equation of a Line Given the Point and the Slope
• Use the Point-Slope Formula:
• is the given point
• Substitute m and into the formula
• Example 1
• Write the equation of the line with slope = -2 and passing through the point ( 3 , -5 ).
y – (-5) = -2 ( x – 3 ) y + 5 = -2x + 6 y = -2x + 1
• Remember this! Parallel lines have the same slope . m = m Perpendicular lines have a slope which is a negative reciprocal of the other. m = - ( 1/m )
• Example 2 Find the equation of a line passing through ( 4,2 ) and parallel to y = 3x + 7. m = 3 x 1 = 4 ; y 1 = 2 y – 2 = 3 (x - 4) y – 2 = 3x - 12 y = 3x -10
• Example 3 Find the equation of a line passing through ( 6,-3 ) and m = 3 perpendicular to y = 3x + 7. m = - 1/3 x 1 = 6 ; y 1 = -3 y – (-3) = -1/3 ( x – 6 ) y + 3 = -1/3 x + 2 y = - 1/3 x - 1
• Seat work: ( ½ crosswise )
• #’s 25, 34, 37 and 40
• Homework: (1/2 crosswise)
• #’s 26, 35, 38 and 41.
• Find the Equation of the Line Given Two Points
• Calculate the slope of the two points.
• Use one of the points and the slope to substitute into the Point-Slope formula.
• Example
• Write the equation of the line that goes through the points (3, 2) and (5, 4).
m = 2/2 or 1 y – 2 = 1 ( x -3 ) y – 2 = x -3 y = x - 1
• Equation of a Line in diff. forms
• Slope – intercept form: y = mx + b
y = x -1 Standard form : Ax + By = C x – y = 1 General form: Ax + By + C = 0 x – y – 1 = 0
• Try this!
• Write the equation of the line that goes through the points (5, 2) and (-3, 7).
• Find the Equation of the Line Given the x - and y - intercepts
• Write the intercepts as ordered pairs.
• The x -intercept 4 is the ordered pair (4, 0).
• The y -intercept -2 is the ordered pair (0, -2).
• Calculate the slope.
• Substitute the slope and the y -intercept ( b ) into the slope-intercept formula.
• Example
• Write the equation of the line with x -intercept 3
• and y -intercept 2.
• x -intercept 3 = (3, 0); y -intercept 2 = (0, 2)
• Slope:
y = mx + b
• Seatwork: (1/2 crosswise)
• Express your answer in different forms of equation. (slope-intercept , standard and general)
• 1.Find the equation of a line which goes through (1,-3) and (-5,2).
• 2. Find the equation of a line with x-intercept of 4 and y-intercept of -16.