Download Day 91 – Slope From 2 Points

FINDING THE
SLOPE FROM
2 POINTS
Day 91
Learning Target:
Students can find the
slope of a line from 2
given points.
Linear equations have constant slope
(or constant rate of change). For a line on
the coordinate plane, slope is the following
ratio:
vertical change
change in y
=
horizontal change
change in x
This ratio is often referred to as rise, or “rise
run
over run,” where rise indicates the number
of units moved up or down and run
indicates the number of units moved to the
left or right. Slope can be positive, negative,
zero, or undefined. A line with positive slope
goes up from left to right. A line with negative
slope goes down from left to right.
Zero Slope
Positive
Slope
Negative
Slope
Undefined Slope
If you know any two points on a
line, you can find the slope of the
line without graphing. The slope of
a line through the points (x1, y1)
and (x2, y2) is as follows:
y2 – y1
x2 – x1
Slope from 2 points Steps:
LABEL, WRITE, PLUG AND CHUG!!
1.
2.
3.
4.
Label points
Write the slope formula
Plug the numbers in the formula
Chug out the answers
Find the slope of the line that passes
through (–2, –3) and (4, 6).
Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6).
y2 – y1 6 – (–3)
x2 – x1 = 4 – (–2)
3
=9
=
6
2
Substitute 6 for y2, –3 for y1,
4 for x2, and –2 for x1.
The slope of the line that passes through
(–2, –3) and (4, 6) is 3.
2
Find the slope of the line that passes
through (–4, –6) and (2, -3).
Let (x1, y1) be (–4, –6) and (x2, y2) be (2, 3).
y2 – y1 3 – (–6)
x2 – x1 = 2 – (–4)
3
=9
=
6
2
Substitute 3 for y2, –6 for y1,
2 for x2, and –4 for x1.
The slope of the line that passes through
(–4, –6) and (2, 3) is 3.
2
Nonlinear equations have
variable rates of change. This
means that the rate of
change is different between
values. This is shown in a
graph by a curved line.
(NONLINEAR)
(LINEAR)
(NONLINEAR)
(NONLINEAR)
(NONLINEAR)
(LINEAR)
Find the slope of the line passing
through each pair of points.
1. (4, 3) and (–1, 1)
2
5
2. (–1, 5) and (4, 2)
–3
5
Ticket Out The Door
• Draw and label the different
types of slope
• What is the slope formula?
• Find the slope from the
points (1,7) and (11,12)