13.2 - Some Applications

Today, we're going to learn about independent and dependent variables. Can someone explain what they understand by these terms?

Correct! The independent variable is the one we control, while the dependent variable depends on it. Can anyone give me an example?

Exactly! In this case, electricity usage is independent, and the bill is dependent. We can visualize this relationship through graphs.

Great question! We’ll plot the independent variable on the x-axis and the dependent variable on the y-axis. This way, we can visualize how changes in one affect the other.

To summarize, independent variables are what we control, while dependent variables are affected by these controls. We will encounter this concept multiple times in our examples.

Now let's look at an example involving petrol. If we have the quantity of petrol and its cost, can anyone tell me how we can plot this?

Correct! And when we plot the points from the table we have, what do we notice?

Yes, excellent observation! This linearity reflects direct variation. In such cases, as one quantity increases, the other does too. Can anyone think of another example where we see a similar relationship?

Exactly! Great example! Both the quantity of deposit and interest are linear, and we can display this on a graph, too.

To conclude, our lessons on quantity and cost will help us interpret various real-life data through graphing!

Let’s apply everything we’ve discussed to time and distance. If Ajit rides his scooter at a constant speed, how can we represent this relationship graphically?

Correct! As time goes on, distance will increase linearly. How can we calculate the distance for a certain amount of time?

Right again! So if he rides for 3 hours, what distance does he cover?

Fantastic! In summary, we use graphs to visualize relationships between different quantities, enhancing our understanding of everyday situations like traveling or spending.