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Parallel Lines

Parallel Lines. We have seen that parallel lines have the same slope. . What will be the slope of the line that is parallel to y=4x-7?. 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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Parallel Lines

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  1. Parallel Lines

  2. We have seen that parallel lines have the same slope.

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

  4. 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.)

  5. Let’s look at how we can write equations of a line parallel to another one going through a certain point.

  6. To write an equation of a line parallel to a given line passing through a given point: • 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’. • 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.

  7. 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.

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

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

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