Page 377 - Algebra 1

When an equation has one variable that is equal to a constant times another variable, the equation represents a direct variation. The equation y = kx, where k is a nonzero constant called the constant of variation, shows a direct variation between x and y.
Direct Variation
Identifying Direct Variation from an Equation
Tell whether each equation represents a direct variation. If the equation is a direct variation, find the constant of variation.
a. y+8x=0
SOLUTION
Transform the equation into y = kx form. y + 8x = 0
y = -8x Subtract 8x from both sides.
This is a direct variation. The constant of variation is -8.
b. _y =x 10
SOLUTION
Representation
Description
equation
y = kx; k is a nonzero constant.
graph
a line that always passes through (0, 0).
words
“y varies directly with x.”
“y is directly proportional to x.”
Example
1
Hint
An equation that represents a direct variation is written in the form y = kx.
Transform the equation into y = kx form. _y = x
10
y = 10x Multiply both sides by 10.
This is a direct variation. The constant of variation is 10.
c. xy=6
SOLUTION
Transform the equation into y = kx form. xy = 6
y = _6 Divide both sides by x. x
This is not a direct variation. The constant is divided by x, not multiplied. It is not in the y = kx form.
Hint
Remember that dividing by a number is the same as multiplying by its reciprocal.
362 Saxon Algebra 1