Linear equation performance task(you are a saint if you do this cluster of a mess)joe took $12 to the arcade. each game cost $.50 to play. this situation can be modeled with theequation y = -.50x + 12. this represents the relationship between money joe has remaining, y,and the number of games he plays, x.a) if joe plays 5 games, how much money does he still have? b) if joe leaves the arcade with $3.50, how many games did he play? c) use the function to determine the y-intercept. state the meaning of the y-intercept in the terms of this problem situationd) use the function to determine the x-intercept. state the meaning of the x-intercept in the terms of this problem situation.e) what is the slope of this equation and what does it mean in the terms of this problem situation? f) state the domain and range for this equation in the context of the problem scenario.domain: range: g) transform the equation into standard form.

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

The answer is a. $1,200. Employee A has 6% commission on all sales. For sale of $100,000 which is 100%, x is the commission of 6%. $100,000 : 100% = x : 6%. x = $100,000 * 6% : 100% = $6,000. Employee B has 4% commission on the first $80,000 and 8% on anything over $80,000. For sale of $80,000 which is 100%, x is the commission of 4%. $80,000 : 100% = x : 4%. x = $80,000 * 4% : 100% = $3,200. For sale of $20,000 which is 100%, x is the commission of 8%. $20,000 : 100% = x : 8%. x = $20,000 * 8% : 100% = $1,600. The total commission for Employee B is $3,200 + $1,600 = $4,800. The difference between Employees A and B is: $6,000 - $4,800 = $1,200.