Question
Using the table of values: (3 points)
x cups of milk y tbl chocolate syrup
2 1
4 2
5 2.5
30 15
What is the slope in context?
What is the y-intercept in context?
What is the equation of the line?
x cups of milk y tbl chocolate syrup
2 1
4 2
5 2.5
30 15
What is the slope in context?
What is the y-intercept in context?
What is the equation of the line?
Answers
GPT 3.5
The slope in context is the rate at which the amount of chocolate syrup increases with each cup of milk.
To find the slope, we can use the formula: slope = change in y/change in x.
From the table, we can observe that when the number of cups of milk increases from 2 to 4, the amount of chocolate syrup increases from 1 to 2. This indicates a change in y of 2 - 1 = 1.
Similarly, when the number of cups of milk increases from 4 to 5, the amount of chocolate syrup increases from 2 to 2.5. This indicates a change in y of 2.5 - 2 = 0.5.
Therefore, the average rate of change of y with respect to x is (1+0.5)/2 = 0.75 over this interval.
The y-intercept in context is the amount of chocolate syrup when there are 0 cups of milk. From the table, we can see that when x = 0, y = 0. This means that the y-intercept is at the origin (0,0).
The equation of the line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Using the values we found, the equation of the line is y = 0.75x.
To find the slope, we can use the formula: slope = change in y/change in x.
From the table, we can observe that when the number of cups of milk increases from 2 to 4, the amount of chocolate syrup increases from 1 to 2. This indicates a change in y of 2 - 1 = 1.
Similarly, when the number of cups of milk increases from 4 to 5, the amount of chocolate syrup increases from 2 to 2.5. This indicates a change in y of 2.5 - 2 = 0.5.
Therefore, the average rate of change of y with respect to x is (1+0.5)/2 = 0.75 over this interval.
The y-intercept in context is the amount of chocolate syrup when there are 0 cups of milk. From the table, we can see that when x = 0, y = 0. This means that the y-intercept is at the origin (0,0).
The equation of the line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Using the values we found, the equation of the line is y = 0.75x.