The document discusses parallel lines and how to find the equation of a line parallel to a given line that passes through a given point. It provides an example, finding the equation of the line parallel to y=3x+6 that passes through the point (-1,9). The slope of any parallel line is the same as the original line. To find the equation, substitute the original slope and point coordinates into y=mx+b and solve for b, then write the full equation with the new b value.

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