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What is the slope of the line? Think about what that means in relationship to the number of meals prepared and number of days.



(1 point)
Responses

-6
-6

(5, 30)
(5, 30)

1/6

6
6
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3 answers

To find the slope of a line, you typically use the formula for slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.

It appears that you have provided some values (including -6 and (5, 30)), but it's unclear what these numbers refer to. If the point (5, 30) represents that on day 5, 30 meals were prepared, we still need at least one more point to calculate the slope.

If you have another point, please provide it. If not, and only the options are given, I can assume you are looking for a conceptual explanation instead.

For example:

  • If the slope is -6, it would mean that as the number of days increases, the number of meals prepared decreases significantly.
  • A slope of 6 would indicate that with each passing day, the number of meals prepared increases significantly.
  • If the slope is 1/6, it would mean that the number of meals prepared increases slowly as the number of days increases.

Please clarify or provide more points so that we can calculate and interpret the slope correctly!

the graph contains a line that starts at (0, 0) and has a point at (5, 30), (10, 60), (90, 15), and lastly (120, 20)

To find the slope of the line that starts at the origin (0, 0) and uses other points, we can select any two points that lie on the same segment of the line.

Let's calculate the slope for the points you provided that seem to be consistent with a line:

  1. Point 1: (0, 0)
  2. Point 2: (5, 30)
  3. Point 3: (10, 60)

Calculating the slope between (0, 0) and (5, 30):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{30 - 0}{5 - 0} = \frac{30}{5} = 6 \]

Calculating the slope between (5, 30) and (10, 60):

\[ m = \frac{60 - 30}{10 - 5} = \frac{30}{5} = 6 \]

Since the slope is the same (6) for these two segments, we can conclude that the slope of the line in this context is:

6

Interpretation:

The slope of 6 means that for every day (each unit increase in x), the number of meals prepared increases by 6 (each unit increase in y). Thus, as the number of days increases, the meals prepared grows consistently.

If you have any further questions or need additional explanations, feel free to ask!