PLEASE HELP, I WILL GIVE BRAINLIEST IF ITS RIGHT :) (03.03 MC)
The table below represents a linear function f(x) and the equation represents a function g(x):

x f(x)
−1 −3
0 0
1 3
g(x)

g(x) = 7x + 2

Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

(10 points)

2.
(03.05 HC)
The table below represents the distance of a train from its destination as a function of time:

Time
(hours)
x Distance
(miles)
y
0 665
1 570
2 475
3 380
4 285

Part A: What is the y-intercept of the function, and what does this tell you about the train? (4 points)

Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours, and tell what the average rate represents. (4 points)

Part C: What would be the domain of the function if the train continued to travel at this rate until it reached its destination? (2 points)

(10 points)

3.
(03.06 MC)
Part A: Billy rented a canoe at $14 for 2 hours. If he rents the same canoe for 5 hours, he has to pay a total rent of $29.

Write an equation in the standard form to represent the total rent (y) that Billy has to pay for renting the canoe for x hours. (4 points)

Part B: Write the equation obtained in Part A using function notation. (2 points)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

(10 points)

9514 1404 393

Step-by-step explanation:

1. (a) The table contains the point (0, 0), and is said to represent a linear function. Consequently, we know that function f is a proportion. Its slope is ...

  y/x = 3/1 = 3.

The slope of function g is the x-coefficient, 7. Since 7 > 3, the slope of function g is greater.

(b) As we said, function f has a y-intercept of 0. The y-intercept of function g is the constant in its equation, 2. Since 2 > 0, the y-intercept of function g is greater.

__

2. (a) The y-intercept is the value when x=0, which is 665. That is the train's initial distance to destination.

(b) The average rate of change from x = 1 to x = 4 is ...

  m = (285 -570)/(4 -1) = -285/3 = -95 . . . . miles per hour

The train's distance to destination is decreasing at 95 miles per hour.

(c) From part B, we know the train covers 285 miles in 3 hours, so the time to destination will be 3 hours more than 4 hours. (Distance is 285 miles at 4 hours.) The useful domain of the relation is 0 ≤ x ≤ 7.

__

3. We can write the standard form equation using the relation ...

  (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

  (29 -14)(x -2) -(5 -2)(y -14) = 0 . . . . . fill in the given points: (2, 14), (5, 29)

  15x -30 -3y +42 = 0 . . . . simpify

  5x -y = -4 . . . . . divide by 3 and subtract 4

(We wonder if "slope-intercept" form is desired: y=5x+4.)

(b) The above equation can be solved for y (by adding y+4), and "y" replaced by "f(x)". The result is the "functional form" ...

  f(x) = 5x +4

(c) The line can be graphed by starting at the y-intercept (0, 4) and drawing a line with slope 5.

Axes will be labeled "Rental Time (hours)" (horizontal) and "Rental Cost (dollars)" (vertical).

Axes can be numbered in units appropriate to the size of the graph. (That will depend on the graph paper or tool used to create the graph.) An example of a graph is attached.

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights