always indicate direct proportion among variables. Observe this graph: The distance travelled and the time taken are proportional, but how do we know that? Note that i) The graph is a straight line. ii) The line passes through the origin.
When both of these features are present we know that the two quantities on the graph must be directly proportional. Do you see this in the graph? Time (in minutes) Distance (in km) If one variable doubles, the other also doubles. From this you can see the relation d = rt and it is easy to guess the constant of proportionality.
( , ) ( , ) ( , ) ( , ) Scale x axis cm = units y axis cm = units Fig. . Time (minutes) Distance (km) Thinking Corner What can you say if the variables x and y are related by the equation y – x = ? It also indicates direct variation.
How? Think about it. In that case, what is the constant of proportionality? y = x Algebra Example .
Varshika drew circles with different sizes. Draw a graph for the relationship between the diameter and circumference (approximately related) of each circle as shown in the table and use it to find the circumference of a circle when its diameter is cm. Diameter (x) cm Circumference (y) cm . .
. . . Solution: From the table, we found that as x increses, y also increases.
Thus, the variation is a direct variation. Let y = kx , where k is a constant of proportionality. From the given values, we have, . .
k When you plot the points ( , . ) ( , . ) ( , . ), ( , .
), ( , . ), you find the relation y = ( . ) x forms a straight-line graph. Clearly, from the graph, when diameter is cm, its circumference is .
cm. Example . A bus is