ACT MATH

LINES

What is the formula for the distance of a line?

What is the formula for the distance of a line?

D =

What is the formula for the distance of a line?

D =

What is the formula for the distance of a line?

D =

What is the formula for the distance of a line?

D =

What is the formula for the distance of a line?

D =

Let’s ask that again:

Let’s ask that again:

What is the formula for the distance of a line?

Let’s ask that again:

What is the formula for the distance of a line?

Say it out loud.

D =

One more time:

One more time:

What is the formula for the distance of a line?

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D =

What is the distance between point A and Point B?

(8,2)

(4,-1)

D = The distance between Point

A and Point B is 5 units

Last time:

What is the formula for the distance of a line?

D =

What is the formula for the midpoint of a line?

,

See if you can say it before going to the next slide.

Did you get it right?

,

What is midpoint between these two points?

(8,2)

(4,-1)

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

What is midpoint between these two points?

(8,2)

(4,-1)

,

The Midpoint

What is the formula for a line?

What is the formula for a line?

𝑦=𝑚𝑥+𝑏

What is the formula for a line?

𝑦=𝒎𝑥+𝑏This is the slope which usually is a

fraction

What is the formula for a line?

𝑦=𝒎𝑥+𝒃This is where the line

crosses the Y Axix

What is the formula for a line?

𝑦=𝒎𝑥+𝟏If the y intercept is 1 then the line goes

through the Y axis at 1.

What is the formula for a line?

𝑦=𝒎𝑥+𝟏If the y intercept is 1 then the line goes

through the Y axis at 1.1

What is the formula for a line?

𝑦=𝒎𝑥+𝟐If the y intercept is 2 then the line goes

through the Y axis at 2

2

What is the formula for a line?

𝑦=𝒎𝑥+𝟑If the y intercept is 3 then the line goes

through the Y axis at 3

3

What is the formula for a line?

𝑦=𝒎𝑥+𝟒If the y intercept is 4 then the line goes

through the Y axis at 4

4

What is the formula for a line?

𝑦=𝒎𝑥+𝟎If the y intercept is 0 then the line goes

through the Y axis at 0

0

Let’s go back to this formula

Let’s go back to this formula

𝑦=𝒎𝑥+𝟏1

The slope is always a fraction.

Let’s go back to this formula

𝑦=𝒎𝑥+𝟏1

Let’s say the slope is 1/2

Let’s go back to this formula

𝑦=𝟏𝟐𝑥+𝟏

1

Let’s say the slope is 1/2

Let’s go back to this formula

𝑦=𝟏𝟐𝑥+𝟏

1

Let’s go back to this formula

𝑦=𝟏𝟐𝑥+𝟏

1

This is the rise

Let’s go back to this formula

𝑦=𝟏𝟐𝑥+𝟏

1

This is the rise

Over the run

Let’s go back to this formula

𝑦=𝟏2𝑥+1

1rise1

Let’s go back to this formula

𝑦=1𝟐𝑥+1

1

run

1

2

1

Let’s go back to this formula

𝑦=1𝟐𝑥+1run

1

2

1

Let’s go back to this formula

𝑦=𝟏𝟐𝑥+1

1

2 1

2

Let’s go back to this formula

𝑦=𝟏𝟐𝑥+1

Let’s go back to this formula

𝑦=12𝑥+𝟏If the y

intercept goes to 0

watch what happens

Let’s go back to this formula

𝑦=12𝑥+𝟎If the y

intercept goes to 0

watch what happens

Let’s go back to this formula

𝑦=12𝑥+𝟎If the y

intercept goes to 0

watch what happens

0

Let’s go back to this formula

𝑦=12𝑥+𝟎If the y

intercept goes to 2

watch what happens

0

Let’s go back to this formula

𝑦=12𝑥+𝟐If the y

intercept goes to 2

watch what happens

0

Let’s go back to this formula

𝑦=12𝑥+𝟐If the y

intercept goes to 2

watch what happens

2

Without going to the next slide can you say what the formula for a line is?

Without going to the next slide can you say what the formula for a line is?

𝒚=𝒎𝒙+𝒃Did you get it right?

What does the “m” mean?

𝒚=𝒎𝒙+𝒃

slope

𝒚=𝟏𝟐𝒙+𝒃

slope

𝒚=𝟏𝟐𝒙+𝒃

1

12

slope

𝒚=𝟏𝟐𝒙+𝒃

1

12

rise

1

slope

𝒚=𝟏𝟐𝒙+𝒃

1

1

2 run

2

slope

𝒚=𝟏𝟐𝒙+𝒃

1

What does the “b” mean?

𝒚=𝑚𝒙+𝒃

Y - intercept

𝒚=𝑚𝒙+𝒃11

2 12

Y - intercept

𝒚=𝑚𝒙+𝟏11

2 12

Where the line crosses the Y axis

𝒚=𝑚𝒙+𝟏11

2 12

Where the line crosses the Y axis

𝒚=𝑚𝒙+𝟏12 1

2

1

What do parallel lines have in common?

Let’s go back to this formula

0

Let’s go back to this formula

0

Let’s go back to this formula

0

𝑦=𝟏𝟐𝑥+𝟏

1

Let’s go back to this formula

0

𝑦=𝟏𝟐𝑥+𝟏

1

0

𝑦=𝟏𝟐𝑥+𝟏

1

𝑦=𝟏𝟐𝑥+𝟐

2

All these slopes are the same because the lines are parallel

0

𝑦=𝟏𝟐𝑥+𝟏

1

𝑦=𝟏𝟐𝑥+𝟐

2

All these slopes are the same because the lines are parallel

0

𝑦=𝟏𝟐𝑥+𝟏

1

𝑦=𝟏𝟐𝑥+𝟐

2

What is the slope of a perpendicular line to the line below?

𝑦=𝟏𝟐𝑥+𝟐

What is the slope of a perpendicular line to the line below?

𝑦=𝟐𝟏𝑥+𝟐

Just flip the slope and then multiply by -1

What is the slope of a perpendicular line to the line below?

𝑦=𝟐𝟏𝑥+𝟐

Just flip the slope and then multiply by -1

What is the slope of a perpendicular line to the line below?

𝑦=−𝟐𝟏𝑥+𝟐

Just flip the slope and then multiply by -1

What is the slope of a perpendicular line to the line below?

𝑦=𝟑𝟒𝑥+𝟐

What is the slope of a perpendicular line to the line below?

−𝟒𝟑𝑥

What is the slope of a perpendicular line to the line below?

𝑦=𝟐 𝑥+𝟐

What is the slope of a perpendicular line to the line below?

−𝟏𝟐𝑥