Ordered Pairs, Intercepts, And Slopes Worksheet Page 3
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18Secton . — Ordered Pars, Intercepts, and Slopes
y
y
(0
2)
,
(0
1)
,
(1
0)
,
x
x
(-1
0)
,
Linear Equation: –2x + y = 2 or y = 2x + 2
Linear Equation: x + y = 1 or y = –x + 1
x-intercept: (–1, 0) y-intercept: (0, 2) slope: 2
x-intercept: (1, 0) y-intercept: (0, 1) slope: –1
Note that when the slope is a positive value, the line extends up, left to right. When the slope is a negative
value, the slope extends down, left to right.
RUN
horizontal
Calculating the Slope of a Line
(x-direction)
It is possible to calculate the slope of a line, if you know two points on that
line (i.e., two solutions to the equation of the line). It is not difficult,
RISE
but does require that you understand what the slope of a line actually
vertical
means. Think of a flight of stairs—each step consists of a riser
(y-direction)
(the vertical part) and the tread (the horizontal part). The flight
of stairs consists of “rises” and “runs.” The slope of the stairs is a
ratio of the rise or vertical change to the run or horizontal change.
You have already learned to calculate the length of both vertical and horizontal line segments; the slope is
simply the vertical length divided by the horizontal length.
y
Let’s look at the slope of a line on the coordinate plane. (The equation
for this line is: y = 2x – 5.)
(2, 3)
In the figure at right, we can see that the rise is the vertical line
(4, 3)
segment that extends from –1 to 3 on the y-axis. We can calculate
the length of this line as |y
– y
| or |3 – (–1)| = 4.
2
1
x
The run is measured on the horizontal line segment that extends
(2, -1)
from 2 to 4 on the x-axis. We can calculate the length of this line
as |x
– x
| or |4 – 2| = 2.
2
2
(
y
-
y
)
4
The ratio of the rise to the run is
, in this case
or 2.
2
1
x
-
x
(
)
2
This is the slope of the line.
2
1
Slope Formula
The Slope Formula allows us to
Given the coordinates of any two points
y
-
y
perform these calculations in one
(
)
m
=
2
1
(x
, y
) and (x
, y
), the slope of their line is:
neat step.
(
x
-
x
)
1
1
2
2
2
1
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education