Final answer:
The independent variable in a factory's car production scenario is the number of hours, while the dependent variable is the number of cars produced. The number of cars depends on the time the factory operates, thus making time the independent variable and car production the dependent variable.
Step-by-step explanation:
In the scenario where a factory produces 10 cars every 3 hours, the independent variable would be the number of hours, and the dependent variable would be the number of cars produced. This is because the number of cars produced depends on the number of hours the factory operates. The factory's production is the outcome that is measured, which makes it the dependent variable, whereas time, which can be set or controlled, is the independent variable.
For a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept, if we were to write an equation for the factory's car production, we would have something like y = ()x + . If we assume that the factory starts producing cars from zero at the beginning of the time measured, then the y-intercept would be 0. The slope would represent the rate of production, in this case, 3.33 cars per hour (10 cars/3 hours).
If you were to graph this relationship, you would plot time on the x-axis and the number of cars produced on the y-axis. You would label each axis accordingly and choose a suitable scale to represent the data. Each unit increase along the x-axis would correspond to 3.33 more cars produced on the y-axis, indicating the constant rate of production represented by the slope of the line.