Parallel LinesParallel Lines

We have seen that parallel lines have We have seen that parallel lines have the the

same slope. same slope.

What will be the slope of the line that What will be the slope of the line that is is

parallel to y=4x-7?parallel to y=4x-7?

What will be the slope of the line that What will be the slope of the line that is is

parallel to y=4x-7?parallel to y=4x-7?

The slope will be 4. (Parallel lines have The slope will be 4. (Parallel lines have

equal slopes.)equal slopes.)

Let’s look at how we can write Let’s look at how we can write equations of equations of

a line parallel to another one going a line parallel to another one going through through

a certain point.a certain point.

To write an equation of a line parallel to a To write an equation of a line parallel to a given line passing through a given point:given line passing through a given point:

1.1. Find the y-intercept of the new line by Find the y-intercept of the new line by substituting the original slope into y=mx+b for substituting the original slope into y=mx+b for

‘m’ ‘m’ and the ‘x’ and ‘y’ coordinates in for ‘x’ and ‘y’ and the ‘x’ and ‘y’ coordinates in for ‘x’ and ‘y’ respectively and solving for ‘b’.respectively and solving for ‘b’.

2.2. Plug the original slope and the new y-intercept Plug the original slope and the new y-intercept into y=mx+b and then you have the equation of into y=mx+b and then you have the equation of the line parallel to the given line through the the line parallel to the given line through the

given given point.point.

Find the equation of the line parallel to Find the equation of the line parallel to

y=3x+6 passing through (-1,9).y=3x+6 passing through (-1,9).

y=mx+by=mx+b9=3(-1)+b9=3(-1)+b Substitute in the slope and the coordinates of the point Substitute in the slope and the coordinates of the point

that it that it passes through.passes through.

12=b12=b Solve for ‘b’.Solve for ‘b’.

y=mx+by=mx+by=3x+12y=3x+12 Plug the slope and the new y-intercept in to find the Plug the slope and the new y-intercept in to find the

new equation.new equation.

Work these on your paper.Work these on your paper.

Write an equation for the lines parallel to Write an equation for the lines parallel to

the given lines and passing through the the given lines and passing through the

given points.given points.

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

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

3.3. y=x-6y=x-6 (2,5)(2,5)

Check your answers.Check your answers.

Write an equation for the lines parallel to Write an equation for the lines parallel to

the given lines and passing through the the given lines and passing through the

given points.given points.

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

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

3.3. y=x-6y=x-6 (2,5)(2,5) y=x+3y=x+3