P 1 2 3 4 q 18 12 6 0

Required:
a. Write an expression for q as a linear function of p.
b. Write an expression for p as a linear function of q

a) An expression for q as a linear function of p is; q = 24 -6p

b) An expression for p as a linear function of q is; p = (24-q)/6

We can write an expression for q in terms of p by evaluating the rate of change as follows;

On this note;

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The answer is below

Step-by-step explanation:

A function shows the relationship that exist between two variables (the independent variable and dependent variable). The independent variable does not depend on any variable and is known as the input while the dependent variable depends on other variable and is known as the output.

The relationship between two variables of a linear function i.e y (dependent variable) and x (independent variable) represented by the points is given by:

a)  Write an expression for q as a linear function of p.

To do this, q is the dependent variable and p is the independent variable. From the table. the variables can be represented by (1, 18) and (2, 12)

Hence:

b)  Write an expression for p as a linear function of q.

To do this, p is the dependent variable and q is the independent variable. From the table. the variables can be represented by (18, 1) and (12, 2)

Hence:

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!