Act math lnes

ACT MATH

LINES

What is the formula for the distance of a line?


D =

Let’s ask that again:



Say it out loud.

One more time:

What is the distance between point A and Point B?

(8,2)

(4,-1)


(8,2)

(4,-1)

D =


(8,2)

(4,-1)

D = The distance between Point

A and Point B is 5 units

Last time:


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)


(8,2)

(4,-1)

,


(8,2)

(4,-1)

,

The Midpoint

What is the formula for a line?


𝑦=𝑚𝑥+𝑏


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

fraction


𝑦=𝒎𝑥+𝒃This is where the line

crosses the Y Axix


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

through the Y axis at 1.


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

through the Y axis at 1.1


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

through the Y axis at 2

2


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


3


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


4


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


0

Let’s go back to this formula


𝑦=𝒎𝑥+𝟏1

The slope is always a fraction.


𝑦=𝒎𝑥+𝟏1

Let’s say the slope is 1/2


𝑦=𝟏𝟐𝑥+𝟏

1

Let’s say the slope is 1/2


𝑦=𝟏𝟐𝑥+𝟏

1


𝑦=𝟏𝟐𝑥+𝟏

1

This is the rise


𝑦=𝟏𝟐𝑥+𝟏

1

This is the rise

Over the run


𝑦=𝟏2𝑥+1

1rise1


𝑦=1𝟐𝑥+1

1

run

1

2

1


𝑦=1𝟐𝑥+1run

1

2

1


𝑦=𝟏𝟐𝑥+1

1

2 1

2


𝑦=𝟏𝟐𝑥+1


𝑦=12𝑥+𝟏If the y

intercept goes to 0

watch what happens


𝑦=12𝑥+𝟎If the y

intercept goes to 0

watch what happens



intercept goes to 0

watch what happens

0



intercept goes to 2

watch what happens

0


𝑦=12𝑥+𝟐If the y

intercept goes to 2

watch what happens

0


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


1

12

slope


1

12

rise

1

slope


1

1

2 run

2

slope


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?


0


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

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

𝑦=𝟏𝟐𝑥+𝟐


𝑦=𝟐𝟏𝑥+𝟐

Just flip the slope and then multiply by -1


𝑦=−𝟐𝟏𝑥+𝟐

Just flip the slope and then multiply by -1


𝑦=𝟑𝟒𝑥+𝟐


−𝟒𝟑𝑥


𝑦=𝟐 𝑥+𝟐


−𝟏𝟐𝑥

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