3a: complete the table with values for x and y that makes this equation true 3x+y=15


3b: create a graph, plot these points, and find the slope of the line that goes through them.

Answer:

  a. see the attachment for the table (also reproduced below)

  b. slope = -3; see the attachment for a graph

Step-by-step explanation:

A table of values for the function can be filled a couple of ways. One way is to draw the graph of the equation, and read the point values from it. Another way is to solve for each of the variables, and use those equations to find the missing table values.

__

Solving the equation for y, we get ...

  3x +y = 15

  y = -3x +15 . . . . . . subtract 3x; this is "point-slope form"

For the purpose of evaluating for different values of x, we can rearrange this a bit to ...

  y = 3(5 -x) . . . . factor out 3

The given table has x-values of 0, 2, 3, 6. The corresponding y-values are ...

  y = 3(5 -{0, 2, 3, 6}) = 3{5, 3, 2, -1} = {15, 9, 6, -3} . . . . for x={0, 2, 3, 6}

Solving the equation for x, we get ...

  y/3 = 5 -x . . . . . divide the above equation by 3

  x = 5 -(y/3) . . . . . add x-(y/3)

For y-values {0, 3, 8}, the corresponding x-values are ...

  x = 5 -{0, 3, 8}/3 = 5 -{0, 1, 8/3} = {5, 4, 7/3} . . . . for y={0, 3, 8}

Then our table of values is ...

  [tex]\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-8}x&2&4&6&0&3&5&7/3\\y&9&3&-3&15&6&0&8\\\cline{1-8}\end{array}[/tex]

__

The points in the above table can be plotted, and the line drawn through them. Sometimes using the points that are farthest apart makes this easier: (0, 15) and (6, -3).

slope

When we solved for y, we had the equation in slope-intercept form. The slope is the x-coefficient in that equation:

  y = -3x +15   ⇒   slope = -3

PLEASE HELP ASAP 40 POINTS!!!!
The results of a random sample of 1,000 people are recorded in Table 1. Use this data to answer the questions that follow.

Table 1

people who wear corrective lenses 762
people who wear glasses 638
people who wear contact lenses 124
Part A
What percentage of Americans would you predict wear corrective lenses?

Part B
What percentage of Americans would you predict wear glasses?

Part C
What percentage of Americans would you predict wear contact lenses?

Part D
There are about 320 million people living in the United States. Of these, how many would you predict wear corrective lenses?

Part E
Of the 320 million people in the United States, how many would you predict wear glasses?

Part F
How many of the 320 million people in the United States would you predict wear contact lenses?

Question 2
A different random sample of 1,000 people yielded the results recorded in table 2. Use this data to answer the questions that follow.

Table 2

people who wear corrective lenses 745
people who wear glasses 618
people who wear contact lenses 127
Part A
What percentage of Americans would you predict wear corrective lenses?

Part B
What percentage of Americans would you predict wear glasses?
Part C
What percentage of Americans would you predict wear contact lenses?

Part D
How many of the 320 million Americans would you predict wear corrective lenses?

Part E
How many of the 320 million Americans would you predict wear glasses?

Part F
How many of the 320 million Americans would you predict wear contact lenses?

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• Let p represent the parking cost.
• Let t represent the ticket cost.
• Let w represent the cost of a bottle of water.
Use the dropdowns to complete the statements.



(A) One way to express the total cost is to find the cost per person for a ticket and water. Then multiply this expression by
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Write the following back to standard form

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