The linear function f(x) = 0.2x + 79 represents the average test score in your math class, where x is the number of the test taken. the linear function g(x) represents the average test score in your science class, where x is the number of the test taken. x g(x) 1 86 2 84 3 82 part a: determine the test average for your math class after completing test 2. (2 points) part b: determine the test average for your science class after completing test 2. (2 points) part c: which class had a higher average after completing test 4? show work to support your answer. (6 points

part a) 79.4

part b) 84

part c) the science score is .2 higher than the math score.

step-by-step explanation:

part a) it wants us to determine the test average for your math class after completing test 2.

f(x)=0.2x+79 represents the average math test score where x the number of test taken.

so we need to replace x with 2:

f(2)=0.2(2)+79

f(2)=.4       +79

f(2)=79.4

the average math test score is 79.4 after test 2 has been taken.

part b) it wants us to determine the test average for your science class after completing test 2.

the table below represents the average test scores,g(x), after x tests have been taken.

x         1             2             3      

y         86         84             82

when x=1, 1 test has been taken and we see the average is y=86.

when x=2, 2 tests have been taken and we see this average is y=84.

when x=3, 3 tests have been taken and we see this average is y=82.

anyways we are looking for the average after 2 tests, so that is 84.

part c)  

the math test average function is f(x)=0.2x+79 where x is the number of tests taken.

f(4)=0.2(4)+79

f(4)=.8       +79

f(4)=79.8

we see the test average for math is 79.8 after 4 math tests.

now our table for the science test averages don't go that high.

we are going to have to find an equation to represent the pattern.   there is a pattern.   the y's are going down by 2 while the x's are going up by 1.

the slope is rise/run.

so the slope here is -2/1=-2.

slope-intercept form of a line is y=mx+b

we are going to use a point on our line along with our slope to find b.

let's use with m=-2 the point (1,86).

86=-2(1)+b

86=-2   +b

add 2 on both sides:

86+2=b

88=b

the equation for our science test average is y=-2x+88 where x represents the number of tests taken.

so what happens after 4 tests, when x=4:

y=-2(4)+88

y=   -8   +88

y=80

the test average for science is 80 after 4 tests.

no let's compare the test scores after 4 tests for the two difference subjects:

math:   79.8

science: 80

the science score is .2 higher than the math score.

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

thats not a system of equations, that is a solution