Write a linear equation in slope-intercept form or standard form to represent each situation. then, explain why your choice is the best representation. mary is selling popcorn for $5 per bucket and hotdogs for $4.75 each. after one hour, she makes $72.50.

5a + 4.75b = 72.50  is the equation in standard form to represent the situation

Let the number of bucket sold be ‘a’ at $5 each and the number of hotdogs sold be ‘b’ at $4.75 each. Then after 1 hour she makes $72.50

So, on the basis of the above problem we can make an equation as follows:-

The equation for number of popcorn and hotdogs sold after 1 hour:

$72.50 = number of bucket sold x price of popcorn per bucket + number of hotdogs sold x price of hotdog

72.50 = 5a + (4.75)b  

5a + 4.75b = 72.50

The above Equation is equivalent to the standard form of linear equation which is Ax + By = C

where A, B, and C are real numbers, and A and B are both not zero

Hence, the best choice is standard form as it has two variables in it we can solve the equation to get the value of variables in it

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!