After 2 week he has used 8 1/2 cups of dog food after 5 week he has used 21 1/4 cups construct a function in the form y =mx+ to represent the amount of dog food used y, after x weeks

y = 4.25x

Step-by-step explanation:

Given that:

After 2 week he has used 8 1/2 cups of dog food after 5 week he has used 21 1/4 cups, we can write this in coordinate form (x, y) where;

y is the amount of dog food

x is the time in weeks

The coordinates are (2, 8 1/2) and (5, 21 1/4)

get the slope m:

m = y2-y1/x2-x1

m = (21 1/4 - 8 1/2)/5-2

m = (85/4-17/2)/3

m = (85-34/4)/3

m = 51/12

m = 4.25

Get the intercept c:

Substitute any of the points say (2, 17/2) and m = 51/12 into the equation

y = mx+c

17/2 = 51/12(2) + c

17/2 = 51/6 + c

c = 17/2 - 51/6

c = 51-51/6

c = 0

Get the required equation:

substitute m - 4.25 and c = 0 into y = mx+c

y = 4.25x + 0

Hence the required equation is y = 4.25x

Part a : Slope is 40 and it interpret the rate of increase of balance in dollars in the account per day.

Part b :  y - 720 = 40(x - 3) ... Point-slope form. 40x - y +600 = 0 ... Standard form. g(x) = 40x + 600 ... Slope-intercept form.

Part c : $880

Step-by-step explanation:

The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:

x  g(x)

0 $600

3 $720

6 $840

Part a : Therefore, the slope of the function will be and it interprets the rate of increase of balance in dollars in the account per day.

Part b : If we denote g(x) = y, then the equation that models the table will be

⇒ y - 720 = 40(x - 3) (1) Point-slope form.

⇒ 40x - y +600 = 0 (2) Standard form.

⇒ y = 40x + 600

⇒ g(x) = 40x + 600 (3) Slope-intercept form.

Part c : From equation (3), the balance in the account after 7 days will be

g(7) = 40(7) + 600 = 280 + 600 = 880 dollars. (Answer)