5-1 Rat e o f Ch an g e an d Sl o p e
/> 1 V
Quick Review
Rate of change shows th e relationship b etw een two
changing quantities. The slope of a line is the ratio of the
vertical change (the rise) to th e horizontal change (the run).slope = fun = , ris e f 2 - 3Tx^x[
The slope of a horizontal line is 0, an d th e slope of a vertical
line is undefined.Ex a m p l e
What is the slope of the line that passes through the points
(1,12) and (6,22)?slope = ^ ~ ^ — 22 ~ 12 = fO — sloPe x2 - x 1 6-1 5 z 2Ex e r c i se s
Find the slope of the line that passes through each pair
of points.
6. (2, 2), (3, 1) 7. (4, 2), (0, 2)
8. (-1,2), (0,5) 9. (-3 ,-2 ), (-3, 2)Find the slope of each line.VLkyj(
/ X
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)5-2 Direct Variation
Quick Review
A f u n c ti o n r e p r e s e n t s a direct variation if it has th e form
y = kx, where k ¥= 0. The coefficient k is th e constant
of variation.Ex a m p l e
Suppose y varies directly with x, and y = 15 w h en x = 5.
Write a direct variation equation that relates x and y. What^
is the value of y w h e n x = 9?y = kx Start w ith the general form of a direct variation.
15 = fc(5) Substitute 5 for x and 15 for y.
3 = k Divide each side by 5 to solve for k.
y = 3x Write an equation. Substitute 3 for k in y = kx.
The equation y = 3x r e la te s x a n d y. W hen x = 9,y= 3(9),
or 27.Ex e r c i s e s
Suppose y varies directly with x. Write a direct variation
equation that relates x and y. Then find the value of y when
x = 7.- y = 8 w h en x = - 4.
- y = 3 w h en x = 9.
13. y = 15 w h en x = 6.
15. y = - 4 w h en x = 4.
For the data in each table, tell whether y varies directly
with x. If it does, write an equation for the direct variation.
16.
HM
-1 -6
2 3
5 12
92417.-3 7.5
-1 2.5
2-5(^5) -1 2.5
354 Chapter 5 Chapter Review