Sure, let's interpret what the slope represents for each case in terms of daily revenue.
#### (a) [tex]\( m = 800 \)[/tex]
The slope ([tex]\(m\)[/tex]) of the line representing the daily revenue is 800. In the context of a linear function, the slope indicates how much the dependent variable ([tex]\(y\)[/tex] for revenue) changes for each unit increase in the independent variable ([tex]\(x\)[/tex] for time in days).
Interpretation:
For [tex]\( m = 800 \)[/tex], the revenue increases by [tex]$800 for each one-day increase in time. This means if you look at the revenue after one more day, you will see an increase of $[/tex]800 compared to the previous day.
#### (b) [tex]\( m = 250 \)[/tex]
For this part, the slope ([tex]\(m\)[/tex]) is 250. Similarly, the slope tells us the rate at which revenue changes with respect to time.
Interpretation:
For [tex]\( m = 250 \)[/tex], the revenue increases by [tex]$250 for each one-day increase in time. Therefore, on each additional day, the daily revenue goes up by $[/tex]250 compared to the day before.
#### (c) [tex]\( m = 0 \)[/tex]
Here the slope ([tex]\(m\)[/tex]) is 0. The slope being zero means that there is no change in the dependent variable ([tex]\(y\)[/tex]) with respect to change in the independent variable ([tex]\(x\)[/tex]).
Interpretation:
For [tex]\( m = 0 \)[/tex], the revenue does not change with a one-day increase in time. This implies that the daily revenue remains constant regardless of the passage of time.
In summary:
- For [tex]\( m = 800 \)[/tex], the daily revenue increases by [tex]$800 each day.
- For \( m = 250 \), the daily revenue increases by $[/tex]250 each day.
- For [tex]\( m = 0 \)[/tex], the daily revenue remains the same each day, with no increase or decrease.
