Question

journal
compare the graph of a ratio relationship with the graph of a relationship that is not represented by a ratio. how are they similar and different? use an example to explain.
remember
you can represent equivalent ratios on a coordinate plane. the ratio \\(\frac{y}{x}\\) is plotted as the ordered pair \\((x, y)\\). the points that represent the equivalent ratios form a straight line that passes through the origin.
practice
create a graph to represent the values shown in each ratio table.
1

weight (pounds)	1	2	4	5

(a) what is the cost for a weight of 3 pounds?
(b) what is the weight for a cost of $21?
2

time (hours)	1	3	5	7

(a) what is the distance at 6 hours?
(b) what is the time at 275 miles?

Explanation:

Problem 1

Part (a)

Step1: Find the rate of cost per pound

From the table, when weight \( x = 1 \) pound, cost \( y = 3 \) dollars. So the rate is \( \frac{y}{x}=\frac{3}{1} = 3 \) dollars per pound.

Step2: Calculate cost for 3 pounds

Using the rate, for \( x = 3 \) pounds, cost \( y=3\times3 = 9 \) dollars.

Step1: Find the rate of cost per pound (same as before, 3 dollars per pound)

Step2: Calculate weight for $21 cost

Let weight be \( x \). We know \( y = 3x \). For \( y = 21 \), solve \( 21=3x \), so \( x=\frac{21}{3}=7 \) pounds.

Step1: Find the rate of distance per hour

From the table, when time \( x = 1 \) hour, distance \( y = 25 \) miles. So the rate is \( \frac{y}{x}=\frac{25}{1}=25 \) miles per hour.

Step2: Calculate distance at 6 hours

Using the rate, for \( x = 6 \) hours, distance \( y = 25\times6=150 \) miles.

Answer:

The cost for a weight of 3 pounds is 9 dollars.

Part (b)