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Transcript

Equations!

Provided with two lines, you can find the slopes of each line. If the slopes of both lines are equal, you know something special about the lines!

After learning about slopes of lines, parallel lines, and perpendicular lines. You should know...

All About Lines

Point-Slope Form

When an equation is in point

slope form, m=slope and a point

on the line is given.

There exists no

rise in horizontal

lines.

Zero divided by anything is 0. Therefore, the slope of a horizontal line is 0.

Slope-Intercept Form

When an equation is in slope-

intercept form, m=slope

and b=the y intercept.

Horizontal Line Form

This is how a horizontal line is expressed.

They have a slope = 0. We will show why!

Special Case:

Vertical Line Form

This is how a vertical line is expressed!

Vertical lines have no slope. We will show why.

There exists no run in vertical lines because the x value never changes.

It is impossible to divide by zero!

Therefore, there does not exist a slope.

If lines have the same slope but also have the same intercepts, then they are not parallel. They are the same line.

Slopes

You can test if lines have the same intercept by manipulating the equations into the slope-intercept form. Then if the intercepts are equal, the lines are the same.

We can also identify slopes when lines are given in equation form!

Parallel

The lines are parallel!

  • The lines never touch.
  • They share no common points.
  • Even if you extend the lines forever, they will still never touch.

Perpendicular

Lines

of

Remember: If you want to

a

Positive and Negative Slopes

l

,

get a slope in the form

b

If a slope is positive, then we say the line is rising.

If a slope is negative, then we say the line is falling.

Positive Slope

Negative Slope

Lines are perpendicular if their slopes are opposites (negative reciprocals of one another).

then you can simply put a 1 on the bottom. Any number divided by 1 is equal to that number!

Lines

Remember the

Slope Formula!

Rise=

Run=

Rise

Slope=

=

Run

Lines

Perpendicular Lines also always intersect in a right angle (90 degree angle).

Also, if the slopes are opposites, then there product will be -1.

The change in y is also known as the rise.

The change in x is also known as the run.

The slope of a line is

the change in y, between two points, divided by the change in x, between two points.

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