1
Name: ______
Mod:______
SLOPE STUDY GUIDE
IMPORTANT
When deciding the slope (or slant) of a line, always read from left to right.
Fill in the blanks with the correct word or words:
1. The slope of any horizontal line, , will always be ______.
2. The slope of a line that slants uphill (from left to right, of course), , will be a
______fraction.
3. The slope of a line that slants downhill (from left to right, of course), , will be a
______fraction.
4. The slope of any vertical line, , will always be ______or ______.
II. For each of the following lines, write a complete sentence telling whether the slope of the line is positive, negative, zero, or undefined (NO SLOPE), and tell why.
EX. 4 5. 6.
The slope of the line is ______
negative because the line ______
slants downhill. ______
7. 8.
______
______
______
III. So far we have only looked at the “sign” of the slope of a line. Now let us consider how you get the actual fraction. We will use the following symbols as a shorthand notation:
m stands for the word “slope”
is the Greek letter, delta, that stands for the words “change in”
The concept of slope has several interpretations. Some of them are listed below:
IV. To find the slope of a line graphically, you first decide if the slope is zero, undefined, positive, or negative – just based on appearance.
· If the slope is positive or negative, pick two points on the line and draw a right triangle (see example on the next page).
· The length of the vertical leg is the “change in y” or .
· The length of the horizontal leg is the “change in x” or .
· Then use the definition:
FIND THE SLOPE OF EACH OF THE FOLLOWING LINES GRAPHICALLY:
EX. 2 9.
10. 11.
Find the slope of the line containing the two given points graphically:
14. ( - 2, 3 ) ( 1, - 2 ) 15. ( 3, 2 ) ( - 3, - 1 )
VI.
17 – 28. Simplify the following expressions in lowest terms (no mixed numbers)
VII. FINDING THE SLOPE OF A LINE BY FORMULA
Since “change in” means to subtract, the following formula should make sense.
· The slope of a line containing two points: is found by:
On the next page, read example 3. Once you understand it, finish example 4.
EX. 3 Find the slope of the line EX. 4 Find the slope of the line
containing: (5, - 2) (- 3, 4) containing: (- 1, 3) (- 2, - 4)
Let = 5, = - 3
= -2, = 4
=
=
m =
The line slants downhill
FIND the slope of the line containing the given points by formula only:
29. (5, 2) (9, 3)
30. (- 3, 0) (4, - 2)
31. (- 6, - 5) (4, 7)
VII. DRAWING LINES WITH GIVEN SLOPE
For each of the following, draw a line through the given point that has the given slope.
( - 1, 2) ( - 2, - 3) ( - 3, 1)
38. ( 1, 4) 39. ( - 1, 1) 40. ( - 1, 3) no slope
IX. EXERCISES
44. Find the slope of each line:
A)
B)
C)
D)
E)
F)
46. Through the given point,
draw and label a line with the given slope:
a) ( - 9, 2) m = 4
b) (0, - 2) m =
c) (- 7, - 3) no slope