You can use any two points on a line to find its slope. Use subscripts
to distinguish betw een th e two points. In th e diagram , (xj, j/j) are
the coordinates of po in t A, an d (x2, y2) are th e coordinates of
point B. To find th e slope of (A B >, you can use th e slope form ula.Key Concept The Slope Formula
slope = — =rise y2 ~~ yi--------, w here x9 - x, =£0
^ run x2 - Xj 1 1
The x-coordinate you use first in th e d en o m in ato r m u st belong to th e sam e ordered
pair as the y-coordinate you use first in th e num erator.(H eq b b Finding Slope Using Points
What is the slope of the line through ( — 1, 0) and (3, — 2)?X 2 X
Ix-J v
y? h- j
vuxvyi)©RIDDED RESPONSEDoes it m atter which
p o in t is (x 1, y 1) an d
w h ich is (x 2, y 2)?
No. You can pick either
point for (x1, y , ) in the
slope form ula. The other
point is then (x2, y 2).You need the slope, so start
w ith the slope form ula.Substitute ( - 1 , 0 ) for (x j, y^ )
and ( 3 , - 2 ) for (x2, y 2).Simplify to find the answer
to place on the grid.-1/2, y 2 ~ Vi
sl°Pe = x ^- /
-2
3 - ( - 1 )-2
4G o t It? 3. a. W hat is the slope of th e line th rough (1, 3) an d (4, —1)?
b. Reasoning Plot th e points in p a rt (a) an d draw a line through them. Does
the slope of th e line look as you expected it to? Explain.Think
Can you generalize
these results?
Yes. All points on a
horizontal line have the
same y-value, so the
slope is always zero.
Finding the slope of a
vertical line always leads
to division by zero. The
slope is always undefined.
Finding Slopes of Horizontal and Vertical Lines
What is the slope of each line?,(-3,2y(^34) ^
,
X
(^02)
(^07) y
(I (^111)
X
4 0
V^1 -l Q\
Let (x1( yj) = ( - 3 , 2) an d (x2, y2) = (2,2).
y2 - yj 2 - 2
slope =
2
0
( 3) ~ 5 _ °
The slope of th e h orizontal line is 0.
Let (x1; y j) = ( - 2 , - 2 ) an d (x2,y 2) = ( - 2 ,1 ).
. T2- y i 1 — (—2) 3
S ° P 8 x2 - x1 -2 - (-2) 0
Division by zero is u ndefined. The
slope of th e vertical line is undefined.
296 Ch ap t er 5 Lin ear Fu n ct io n s