Nancy is curious if the consumption of sweets, mainly donuts, increases as people get older. Nancy asked 200 customers at a local Krispy Kreme how many donuts they eat in a month, y, and recorded their age, x. She obtained the following regression line y=47-1.36x. What is the meaning of the slope of this regression line

The slope means that the number of donuts reduces by 1.36 as people get older.

A linear equation is in the form:

y = mx + b;

where y, x are variable, m is the slope of the line and b is the y intercept.

Let y represent the number of donut ate by the customers in a month and x represent their age

Given the regression line:

y = 47 - 1.36x

The slope means that the number of donuts reduces by 1.36 as people get older.

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Kindly check explanation

Step-by-step explanation:

Given that:

Number of donuts consumed in a month = y

Age = x

Regression equation obtained :

y=47-1.36x

Meaning of slope of the regression line ;

Comparing the regression equation obtained with the general equation of a linear regression line ;

y = mx + c; where m = slope of the regression line

Hence, the value of slope in the equation is = - 1.36

Thus, the slope can be interpreted as ; The number of donuts consumed in a month is expected to decrease by 1.36 for per(1) increase in age x of consumer.

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24