You work for a manufacturing company on a production line that manufactures cell phones. You are paid $20 a day plus $1.50 for each phone that you assemble. Interpret the slope and y -intercept of the equation of the trend line y=1.50x+20 .
In the equation of the trend line y = 1.50x + 20, the slope represents the change in the dependent variable (y) for each unit increase in the independent variable (x).
In this case, the slope is 1.50, which means that for every phone assembled (x), your pay (y) increases by $1.50.
The y-intercept of the equation (20) represents the starting value of the dependent variable (y) when the independent variable (x) is zero. In this context, it means that even if you haven't assembled any phones, you will still get paid $20 per day.
In the given equation of the trend line, y = 1.50x + 20, x represents the number of phones assembled and y represents the total amount of money earned in a day.
The slope of the equation is 1.50, which means that for every additional phone assembled (x), the total amount of money earned (y) increases by $1.50. This represents the additional income earned per phone assembled. In other words, the slope of 1.50 indicates the incremental increase in earnings for each additional unit produced.
The y-intercept of the equation is 20, which represents the base pay of $20 received each day, regardless of the number of phones assembled. Even if no phones are assembled (x = 0), the worker would still earn $20 as the base pay. Hence, the y-intercept represents the fixed salary received by the worker.
In summary, the equation y = 1.50x + 20 represents the relationship between the number of phones assembled (x) and the total earnings (y) in a day. The slope of 1.50 represents the additional earnings per phone, while the y-intercept of 20 represents the base salary.
To interpret the slope and y-intercept of the equation of the trend line y = 1.50x + 20 in the context of your manufacturing job, you need to understand what each component represents.
In this equation, "y" represents the total amount of money you are paid, and "x" represents the number of cell phones you assemble.
The slope of the equation, which is 1.50, represents the additional amount earned per phone assembled. So, for every additional phone you assemble, you will earn an extra $1.50.
The y-intercept of the equation, which is 20, represents the base pay. It is the amount you would earn if you did not assemble any phones at all. In other words, it is the fixed amount of $20 per day that you receive regardless of the number of phones you assemble.
So, in summary, the interpretation of the equation in the context of your job is as follows:
- For each phone you assemble, you will earn an additional $1.50.
- Even if you don't assemble any phones, you will still receive a fixed payment of $20 per day.
This equation allows you to calculate your total earnings based on the number of phones assembled. By substituting different values of "x" into the equation, you can determine how much you would earn for different production levels.