Page 379 - Algebra 1

Writing and Solving a Direct Variation Equation
The distance a person runs varies directly with the time spent running. If a person runs 12 miles in 2 hours, how many miles will the person run in 3 hours?
SOLUTION
Method1: Becausedistanceyvariesdirectlywithtimex,thegivenpoint is (2, 12).
Example
4
y = kx 12 = k · 2
6=k y = 6x
y=6·3
y = 18 miles
Begin with the equation for direct variation.
Substitute the x- and y-values from the point.
Divide both sides by 2 to solve for k.
Write the direct variation equation with the constant of variation, k.
Substitute 3 for x.
Simplify and label the answer.
Method2: Useaproportion.
_12 = _m 23
12 · 3 = 2m 18 = m
Set up a proportion.
Cross multiply.
Divide both sides by 2 and simplify.
She will run 18 miles in 3 hours.
Graphing a Direct Variation
The grocery store sells 3 pounds of lemons for $1.00. Graph the relationship, and then use the graph to estimate the cost of 12 pounds of lemons.
SOLUTION Start with the point (3, 1.00). Choose another x-value. Use a proportion to find the corresponding y-value.
Example
5
Math Reasoning
Write Why does the graph stop at (0, 0)?
Let x = 12. _1 = _y
3 12 12 · 1 = 3y
Set up a proportion.
Cross multiply.
Divide both sides by 3 and simplify.
4 = y
The second point is (12, 4).
364 Saxon Algebra 1
Graph the two points and draw a line through them.
On the graph, find the y value when x = 12. When x = 12, the y value is 4.
So, the cost of 12 pounds of lemons
is $4.00.
5 4 3 2 1 0
2 4 6 8 10 12 14 Pounds of Lemons
Dollars