Areas, Slopes,

1
Areas, Slopes, Labeling Curves

• Graph Interpretation Notes

2
Slope of a Graph
Slope 0 Slope is Slope is -
Slope is
3
Linear Relationship

• Graph is a straight line
• Possible equations
• y mx b
• y ax

4
Direct Relationship

• As one variable rises, the other rises also
• Slope of graph is positive
• Linear and quadratic (parabola) relationships can
  be direct

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Indirect Relationship

• As one variable increases, the other one
  decreases
• Slope of graph negative
• Inverse is special case takes on shape of
  hyperbola
• y a/x
• xy a

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Quadratic Relationship

• One variable changes with the square of the other
• Also called power relationship
• Graphs are parabolic
• y ax2 bx c
• y x2
• x y2

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Finding Area Beneath Curve
8

• Use A l x w and
• A ½ b x h to arrive at estimate of area
  beneath curve
• Use for total displacement in v vs. t graph or
  change in velocity in an a vs. t graph

Velocity (m/s)
2
8
Time (s)
8
Finding Area Beneath Curve
Area beneath v vs. t graph is displacement AreaTo
tal A? A? ½ bh lw ½ (8 s)(6 m/s)
(8 s)(2 m/s) 24 m 16 m 40 m
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Velocity (m/s)
2
8
Time (s)
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Finding Slope of Graph
If linear graph

• Locate 2 points on graph line, label as points 1
  and 2
• Find x and y coordinates of each point
• 3. Perform slope calculation
• m (y2 y1) / (x2 x1)
• (3-8) / (73)
• -5/4
• m -1.25

Point 1
8
(3,8)
y
Point 2
(7,3)
3
0
USE FOR AVE VELOCITY OUT OF x vs. t GRAPH OR
AVE ACCEL. OUT OF v vs. t GRAPH
3
7
x
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Finding Slope of Graph
Problem Find the slope of the graph at x 5.
1. Extend a tangent line from the curve at the
point slope is desired. 2. Find two points along
tangent line and list their ordered pairs.
(7,18)
10
(3,0)
USE FOR INSTANTANEOUS VELOCITY OUT OF x vs. t
GRAPH OR INSTANTANEOUS ACCELERATION OUT OF v vs.
t GRAPH
5
11
Finding Slope of Graph
Problem Find the slope of the graph at x 5.
(7,18)

• 1. Extend a tangent line from the curve at the
  point slope is desired.
• Find two points along tangent line and list their
  ordered pairs.
• Perform slope calculation
• m (y2 y1) (18-0) 4.5
• (x2 x1) (7-3)

10
(3,0)
5