Me asap < 3
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: find and interpret the slope of the function. (3 points)
part b: write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)
part c: write the equation of the line using function notation. (2 points)
part d: what is the balance in the bank account after 7 days? (2 points)

part a: the slope of the function is -75

part b:

point-slope form is y - 1350 = -75(x - 2)

slope-intercept form is y = -75x + 1500

standard form is 75x + y = 1500

part c: the function notation of the line is g(x) = -75x + 1500

part d: the balance in the account after 5 days is $1125

step-by-step explanation:

* lets explain how to solve the problem

- g(x) is a linear function, where x is the number of days that have

  passed and g(x) is the balance in the bank account

∵ at x = 0 ⇒ g(x) = $1500

∵ at x = 2 ⇒ g(x) = $1350

∵ at x = 4 ⇒ g(x) = $1200

- lets consider the points (0 , 1500) , (2 , 1350) , (4 , 1200) are points

  lie on the line which represents the function g(x)

- the slope of the line which passes through points (x1 , y1) , (x2 , y2)

  is

# part a:

∵ the line passes through (2 , 1350) and (4 , 1200)

∴ x1 = 2 , x2 = 4 and y1 = 1350 , y2 = 1200

∴

∴ the slope of the function is -75

# part b:

∵ the form of point-slope is   , where m is

    the slope of the line and (x1 , y1) is a point on the line

- you can chose any point from the 3 points as (x1 , y1)

∵ m = -75

∵ (2 , 1350) is (x1 , y1)

∴ y - 1350 = -75(x - 2)

* point-slope form is y - 1350 = -75(x - 2)

∵ the form of slope-intercept is y = mx + c , where m is the slope of

    the line and c is the y-intercept

- the y-intercept means the line intersect the y-axis at point (0 , c)

∵ m = -75

∵ point (0 , 1500) is on the line

∴ c = 1500

∴ y = -75x + 1500

* slope-intercept form is y = -75x + 1500

∵ the standard form is ax + by = c , where a , b , c are integers

∵ y = -75 x + 1500

- add 75x to both sides

∴ 75x + y = 1500

* standard form is 75x + y = 1500

# part c:

∵ the function notation of a line is g(x) = mx + c

∵ the equation of the line is y = -75x + 1500

∴ g(x) = -75x + 1500

* the function notation of the line is g(x) = -75x + 1500

# part d:

∵ x represents the number of days that have passed

∴ x = 5

∵ g(x) is the balance in the account

∴ g(5) = -75(5) + 1500

∴ g(5) = -375 + 1500

∴ g(5) = 1125

* the balance in the account after 5 days is $1125

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step-by-step explanation:

the number 100 represents the number of trials in the experiment.

49/100 represents the experimental probability of the coin landing heads up.

step-by-step explanation: