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UNIT 1B LESSON 1Review of Slope

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Slope of a LineThe term slope is often used to describe steepness or rate of change.

The pitch of a roof, the steepness of a ski run, the speed of a car are all examples of slope. In each case, the slope is the ratio of the rise to the run

In a coordinate system, we can determine the slope of any line segment from its endpoints P1(x1, y1) and P2(x2, y2).

From P1 to P2:

• the rise is the difference in the y-coordinates: y2 – y1 or ∆y • the run is the difference in the x-coordinates: x2 – x1 or ∆x

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Slope of a Line

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Slope of a Line

A line that goes uphill as x increases has a positive slope..

A line that goes downhill as x increases has a negative slope.

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Slope of a Line

A horizontal line has slope zero since all of its points have the samey-coordinate.

For vertical lines, the slope is undefined since all of its points havethe same x-coordinate

P1(-1, 1) P2(2, 1)

P1 (1.5, 2)

P2 (1.5, -1)

𝒎=𝟏−𝟏

𝟐−(−𝟏)=𝟎𝟑

=𝟎

division by 0 is undefined

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Parallel LinesParallel lines form equal angles with the x-axis.

Hence, non-vertical parallel lines have the same slope.m1 = m2

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Perpendicular LinesIf two non-vertical lines L1 and L2 are perpendicular, their slopes m1 and m2 satisfy m1m2 = – 1, so each slope is the negative reciprocal of the other:

Line 1 Slope =

Line 2 Slope =

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× −13=−1

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A(2, 1), B(5, 3)

C(– 2, 2), D(1, 4)

Lines that are higher on the right have a positive slope.

   

Lines that have equal slopes are parallel AB // CD and EF // GH

 

𝒎=𝟏−𝟑𝟐−𝟓

=−𝟐−𝟑

=𝟐𝟑

𝒎=𝟐−𝟒

−𝟐−𝟏=

−𝟐−𝟑

=𝟐𝟑

UNIT 1B L1 REVIEW OF SLOPE PAGE 1

Rise = 2

Rise = 2

Run = 3

Run = 3

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E(– 3 , 4), F(– 1 , – 2)

G(0, 5), H(1, 2)

𝒎=𝟒−(−𝟐)

−𝟑−(−𝟏)= 𝟔

−𝟐=−𝟑

𝒎=𝟓−𝟐𝟎−𝟏

=𝟑

−𝟏=−𝟑

Lines that are higher on the left have a negative slope.

   

Lines that have equal slopes are parallel AB // CD and EF // GH

 

Rise = 3

Run = – 1

Rise = – 6

Run = 2

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J(3 , –2), K(6 , – 4)

L(4, –3), M(2, –6)

𝒎=−𝟐−(−𝟒)𝟑−𝟔

= 𝟐−𝟑

=−𝟐𝟑

𝒎=−𝟑−(−𝟔)𝟒−𝟐

=𝟑𝟐

If the slopes of 2 lines are negative reciprocals (product = – 1) they are perpendicular.

JK ┴ LM 

−𝟐𝟑

×𝟑𝟐

=−𝟏

Rise = 2

Run = –3

Rise = 3

Run = 2

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R(– 2 , 4), S(5 , 4)

P(– 3, – 2 ), Q(– 3, 3)

𝒎=𝟒−𝟒

−𝟐−𝟓=

𝟎−𝟕

=𝟎

÷ by 0 is undefined

Horizontal lines will always have a slope of zero Vertical lines will always have a slope which is undefined.  

They are also perpendicular

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QUESTION 9: Two students entered a car rally. During part of the rally, they had to drive at a constant speed. The following graph shows the distance traveled over a given time while traveling at this constant speed.

Distance (km)

Time (hours)

P2

P1

What is the slope of the line and what does it represent?

Slope = (180 km – 60 km) = 60 km/h(3 h – 1 h)

It represents the velocity of the car.

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QUESTION 10The pool at a fitness club is being drained. The graph shows the number of kilolitres of water remaining after an elapsed time.

a) What is the slope of the line and what does it represent?

Slope = (40 kL – 100kL) (240 min – 0 min) = – 0.25kL/min

The pool is draining at a rate of 0.25 kL/min

b) What is the intercept along the vertical axis and what does this intercept represent?

The vertical intercept is (0, 100)

The pool has 100 kL in it before it is drained.

c) What is the intercept along the horizontal axis and what does this intercept represent?

The horizontal intercept is (400, 0)

It takes 400 min to drain the pool.