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.. (image below)

Well, See explanations.

Step-by-step explanation:

Form a table as;

___|

x         g(x)

0       $1500

2       $1350

4        $1200

a) Find the slope, m which is Δy/Δx

m=Δy/Δx

Δy =1350-1500= -150

Δx = 2-0 = 2

m= -150/ 2= -75

This means the balance $ 1500 reduces by $75 after a day

(b) (i) in point slope form

y-y₁=m(x-x₁)

 y-1500= -75( x-0)

(ii) in slope-intercept form

 y=mx+c

 y= -75x +1500

(iii) in standard form

 Ax+By=C  where x and y are variables where as A,B,C are integers

y+75x =1500

(c). Writing the equation in function notation

 f(x)= -75 x +1500

(d) The balance in account after 12 days will be;

  f(12) = -75 *12 +1500  = -900 +1500

 = $ 600

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step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.