4.5 Graphing Activity: Slope- Intercept Form
Equation
Value of
m
Value of
b
1
Graph
Section #1: Slope
x-intercept
y-intercept
Positive or
negative slope
0
(0,0)
(0,0)
positive
2
0
(0,0)
(0,0)
positive
5
0
(0,0)
(0,0)
positive
0
(0,0)
(0,0)
positive
–3
0
(0,0)
(0,0)
negative
–
0
(0,0)
(0,0)
negative
1. y = x
2. y = 2x
3. y = 5x
4. y = x
5. y = –3x
6. y = – x
Use your graphs to answer the following questions:
1. What point do all the graph have in common?
All graphs are passing through (0,0)
2. Look at graphs #1, 2, and 3.
What is happening to the value of m?
The value of m increases
What is happening to the graphs?
The slope (steepness) of the graphs is increasing
3. Look at graphs #1 and 4.
What is happening to the value of m?
The value of m decreases
What is happening to the graphs?
The slope (steepness) of the graphs is decreasing
4. Compare the graphs in #5 and 6 to the line y = –x (build it in #5 with - - - - line)
What is happening to the value of m?
m is negative
What is happening to the graphs?
The slope is negative
Negative m
5. Can you come up with a single rule to explain all of the above?
m = −3
Positive m
m=4
m=1
If b = 0 all graphs pass through he origin.
Positive m will define positive slope, negative m- negative slope.
As the absolute value of m increases, the slope will be steeper,
m=
The graph will lean toward y-axis. Lower values of m will give less
m=−
steep graph that leans toward x-axis.
m=−1
Section #2: y-intercept
Equation
Value of
m
Value of
b
1
0
1
Graph
x-intercept
y-intercept
Positive or
negative slope
(0,0)
(0,0)
positive
3
(0, 3)
positive
1
−4
(0, −4)
positive
1
−2
(0, −2)
positive
−2
4
(0, 4)
negative
1. y = x
2. y = x + 3
3. y = x – 4
4. y = x – 2
5. y = –2x + 4
6.
y = 4x – 2
(0, −2)
4
−2
positive
Use you graphs to answer the following questions:
1. For positive values of b, is the y-intercept above or below the x- axis? above
2. For negative values of b, is the y-intercept above or below the x- axis? below
3. What do you think is b’s job in the equation y = mx + b? to represent vertical shift of the graph
Check your answer by looking at the equation y = –2x + 4
Look at graphs # 1, 2, and 3
4. What is the same about all three graphs?
The slope is the same
5. These lines never intersect so we say they are _parallel_ lines.
6. What is the relationship between b and x-intercepts (where the graph crosses the x-axis) of the
equations? none
Now try some on your own by hand.
Steps: 1) Make sure that the equation is in y = mx + b form. If not, rewrite it
2) State what m = ______ and b = _______
3) BEGIN with b (plot b as the y-intercept on the graph)
4) MOVE the m (count the slope from the b point as many times as you can before going off the graph)
5) connect the points on the line.
1.
y = 2x – 3
m = _2__ b = _−3_
2.
y= x+2
m = __ __
b = _2__
3.
y=
m=_ _
x+5
b = _5__