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. Lets 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: 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.

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. 1. y=1/2x-4(4,2) 2. y=-2x+3(1,2) 3. 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. 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