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Parallel Lines

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We have seen that parallel lines have the same slope.

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What will be the slope of the line that is parallel to y=4x-7?

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What will be the slope of the line that is parallel to y=4x-7? The slope will be 4. (Parallel lines have equal slopes.)

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Lets look at how we can write equations of a line parallel to another one going through a certain point.

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To write an equation of a line parallel to a given line passing through a given point: 1. Find the y-intercept of the new line by substituting the original slope into y=mx+b for m and the x and y coordinates in for x and y respectively and solving for b. 2. Plug the original slope and the new y-intercept into y=mx+b and then you have the equation of the line parallel to the given line through the given point.

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Find the equation of the line parallel to y=3x+6 passing through (-1,9). y=mx+b 9=3(-1)+b Substitute in the slope and the coordinates of the point that it passes through. 12=b Solve for b. y=mx+b y=3x+12 Plug the slope and the new y-intercept in to find the new equation.

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Work these on your paper. Write an equation for the lines parallel to the given lines and passing through the given points. 1. y=1/2x-4(4,2) 2. y=-2x+3(1,2) 3. y=x-6(2,5)

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Check your answers. Write an equation for the lines parallel to the given lines and passing through the given points. 1. y=1/2x-4(4,3)y=1/2x+1 2. y=-2x+3(1,2)y=-2x+4 3. y=x-6(2,5)y=x+3

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