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ACT Math Lines
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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
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