Download Section 4.2 Direct Variation and Slope

Algebra 1 A
Chapter 4
Section 2
Slope and Direct Variation
1
Direct Variation: describes an equation of
the form y = kx, where k  0. k is called the
constant of variation
Key words:
Varies directly
Examples:
y  7.25 x
y
 12
x
always crosses at the point
(0, 0) and it is always a
straight line.
Name the constant of variation of the equation.
Then find the slope of the line and write the
equation
Slope = constant of variation
Pick 2 points and find the slope
Use the slope formula or the
triangle method
Slope = 3
y = 3x
2
Example #2
Name the constant of variation of the equation.
Then find the slope of the line and write the
equation
Pick 2 points and find the slope
Use the slope formula or the
triangle method
Slope = -5/2
y = -2.5x
Graph the direct variation
y = (2/3)x
Y= (2/3)x
Start at the point( 0, 0)
Use the constant of variation
to find the next point
3
Ok so if we use y = x as a our parent graph
What effect does the constant of variation
have on the graph?
Calc activity on page 197 ( next slide)
4
Suppose y varies directly as x, and y = 28 when x = 7
a. find the direct variation equation that relates x and y.
y = kx
28 = k(7)
Substitute 28 for y and 7 for x
4=k
So y = 4x
b. Use the direct variation equation to find x when y = 52
use y = 4x
Substitute 52 for y and solve for x
52 = 4x
13 = x
Therefore , x = 13 when y = 52.
Travel
The Ramirez family is driving cross-country on
vacation. They drive 330 miles in 5.5 hours.
a. Write the direct variation equation to find
distance driven for any number of hours.
d = 60t
b. Graph the equation
Graph left blank on purpose
5
Travel
The Ramirez family is driving cross-country on
vacation. They drive 330 miles in 5.5 hours.
a. Write the direct variation equation to find
distance driven for any number of hours.
d = 60t
b. Graph the equation
c. Estimate how many hours it would take them
to drive 600 miles.
10 hours
6