Step-by-step explanation:
the slope intercept form is
y = ax + b
"a" being the slope, "b" being the y- intercept (which is the y-value when x = 0).
the slope here :
in the table x is always increasing by 2.
and y is always investing by 1.
so, the slope is 1/2
the y-intercept :
we need to find the y-value for x = 0.
but we don't have a data point with x = 0 in the table.
so, we have to extend the structure of the table to the left.
x decreases by 2 (making it 0), and y decreases by 1 (making it -1).
therefore, the y- intercept (b) is -1.
and the line equation is
y = (1/2)x - 1
not sure about "the other method".
there is the point-slope form of the equation :
y - y1 = a(x - x1)
again with "a" begin the slope, and (x1, y1) being a point on the line.
if we get the y-intercept in the table, then this point is (0, y1).
and the equation would be
y - y1 = ax
in our case
y + 1 = (1/2)x
and another method ?
sometimes people write
nx + my = c
in our case starting with the original equation
y = (1/2)x - 1
2y = x - 2
-x + 2y = -2
x - 2y = 2
G(f(2)) means work out whatever f(2) is then plug this into g(x).
So f(2) is 3 because we just find the x-value 2 in the left hand column and read across. This is 3.
So then we find g(3) by finding the x-value 3 in the left hand column and read across. This is 10.
So g(f(2)) = 10
Answers: A) $44,944
B) $50,499.0784
Math: Using the percentage calculator linked below 6% of $40,000 is $2,400. Since you're getting your second raise after your first and since it is a 6% raise from what you're getting paid at that time we add pay raise 1 to your starting pay before calculating the 6% for pay raise 2. $40,000+$2,400=$42,400. 6% of $42,400 is $2,544. $42,400+$2,544=$44,944, Since that is two pay raises that would be your earnings at the end of year two (answer A).
We continue calculating 6% then adding that onto the total before calculating it for the next year for problem B.
6% of $44,944 is $2,696.64. $44,944+$2,696.64=$47,640.64.
6% of $47,640.64 is $2,858.4384. $47,640.64+$2,858.4384=$50,499.0784. That's answer B.
Hopefully you can figure out C on your own! I feel a little bad for giving a partial answer but I think you can do this!
Percentage calculator used-https://percentagecalculator.net/
Note: can't handle commas, remove all commas before entering data in.
