Bell Work
Graph the equation y=2x+4.
(Hint: Use a function table to
determine the ordered pairs.)
Objective

Learn to determine the slope of a line and
recognize constant and variable rates of
change.
Vocabulary

Slope – the measure of the steepness of a
line.
slope = ______ = _________________

Rate of Change – the ratio of two
quantities that change. (i.e. slope)
Slope
The slope of a line is a measure of its steepness
and is the ratio of rise to run:
y
Run
Rise
x
If a line rises from left to right, its slope is positive.
If a line falls from left to right, its slope negative.
Slope
Tell whether the slope is positive or negative.
Then find the slope.
The line rises from left to right.
The slope is positive.
Slope
Tell whether the slope is positive or negative.
Then find the slope.
3
3
The rise is 3. The run is 3.
slope = rise = 3 = 1
3
run
Slope
Tell whether the slope is positive or negative.
Then find the slope.
y
2
–2 0
–2
2
x
The line falls from right to left.
The slope is negative.
Slope
Tell whether the slope is positive or negative.
Then find the slope.
y
2
–2 0
–2
-3
2
2
x
The rise is 2. The run is -3.
slope =
rise = 2
run
-3
Hmmmm….
Tell whether the slope is positive or negative.
Then find the slope.
The line does not point upward or downward so it
is not positive or negative.
Hmmmm….
Tell whether the slope is positive or negative.
Then find the slope.
2
M(1, –1) N(3, –1)
The rise is 0. The run is 2.
slope = rise = 0 = 0
2
run
Notes
You can graph a line if you know its slope and
one of its points.
Slope and a Point
Use the slope  2 and the point (1, –1) to graph
1
the line.
rise = -2 or 2
run
1 -1
From point (1, 1) move 2
units down and 1 unit
right, or move 2 units up
and 1 unit left. Mark the
point where you end up,
and draw a line through the
two points.
y
4
2
●
–4 –2 0
–2
–4
x
2
●
4
Slope and a Point
Use the slope 1 and the point (–1, –1) to
graph the line.2
rise = 1
run
2
From point (–1, –1) move 1
unit up and 2 units right.
Mark the point where you
end up, and draw a line
through the two points.
y
4
2
–4 –2 0
–2
–4
●
x
2
4
Slope and a Point
Use the slope – 2 and the point (2, 0) to graph
3
the line.
rise = -2 or 2
run
3 -3
From point (2, 0) move 2
units down and 3 units
right, or move 2 units up
and 3 unit left. Mark the
point where you end up,
and draw a line through the
two points.
y
4
●2
–4 –2 0
–2
–4
x
2
4
●
Rate of Change
The ratio of two quantities that change, such
as slope, is a rate of change.
A constant rate of change describes changes
of the same amount during equal intervals.
A variable rate of change describes changes
of a different amount during equal intervals.
The graph of a constant rate of change is a
line, and the graph of a variable rate of
change is not a line.
Constant or Variable?
Tell whether each graph shows a constant or
variable rate of change.
A.
B.
The graph is nonlinear,
so the rate of change is
variable.
The graph is linear, so
the rate of change is
constant.
Constant or Variable?
Tell whether each graph shows a constant or
variable rate of change.
y
A.
B.
4
2
–4 –2 0
–2
2
4
x
–4
The graph is nonlinear,
so the rate of change is
variable.
y
4
2
–4 –2 0
–2
2
4
x
–4
The graph is linear, so
the rate of change is
constant.
Butterflies
The graph shows the distance a monarch
butterfly travels overtime. Tell whether the
graph shows a constant or variable rate of
change. Then find how fast the butterfly is
traveling.