Answer:
1) The linear equation in point and slope form is y - 67 = -4 × (x - 14)
2) The variables are;
a) The number of candies available = y
b) The number of days Jennifer eats the candies =
c) The slope, m = -4
3) Jennifer received 123 pieces of candies on Halloween
Step-by-step explanation:
The given parameters are;
The number of candies Jennifer eats everyday = 4 pieces
The number of days for which Jennifer eats the daily 4 candies = 14
The number of candies left at the end of the 14th day = 67 candies
1) We note that the rate of decrease in the number of candies = 4 candies/day
Therefore, the slope of the linear equation is m = -4
The y-intercept = The initial amount of candies Jennifer has = c = 67 + 14× 4 = 123 candies
The linear equation in point and slope form is given as follows;
y - 67 = -4 × (x - 14)
2) The variables are;
a) The y-value represents the number of candies available on a specific day
b) The x value represents the number of days Jennifer eats the candies'
c) The slope = The rate of decrease in the number of candies per day = -4
3) The number of candies Jennifer receives on Halloween is given by the y-intercept of the straight line equation as follows;
y - 67 = -4 × (x - 14)
y - 67 = -4·x + 56
y = -4·x + 56 + 67 = -4·x + 123
y = -4·x + 123
Comparing the above equation, with the general form of the straight line equation, y = m·x + c, where, the constant term, c = The y-intercept, we have;
The y-intercept of the equation y = -4·x + 123 = 123 = The initial amount of candies Jennifer received on Halloween.
-th partial sum is