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

read more on -

step-by-step explanation:

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)