Using the table of values: (3 points)
x cups of milk
2, 4, 5, 30.
y tbl chocolate syrup
1, 2, 2.5, 15.
1) What is the slope in context?
2) What is the y-intercept in context? 1 tbl syrup to 2 cups of milk, or no cups of milk, no syrup
3) What is the equation of the line? y = 2x + 1, or y = 1/2x
1) The slope in context is the rate at which the amount of chocolate syrup changes with respect to the amount of milk. It represents the ratio of the change in y (chocolate syrup) to the change in x (milk). To calculate the slope, we can choose any two points from the table and use the formula:
slope = (change in y) / (change in x)
Let's choose the points (2, 1) and (5, 2.5) from the table.
change in y = 2.5 - 1 = 1.5
change in x = 5 - 2 = 3
slope = 1.5 / 3 = 0.5
So, the slope in context is 0.5 tablespoons of chocolate syrup per cup of milk.
2) The y-intercept in context represents the amount of chocolate syrup when there are no cups of milk. Looking at the table, we can see that when x = 0 (no cups of milk), y = 0 tablespoons of chocolate syrup. Therefore, the y-intercept is 0.
3) The equation of the line can be determined using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Substituting the values we found:
y = 0.5x + 0
Simplifying, we get:
y = 0.5x
Alternatively, we can write it as y = 1/2x.