QuestionEach Friday, 400 newsletters are printed. The equation $c=400 w$ relates weeks $w$ to total copies $c$ . What is true of the graph?

Studdy Solution

STEP 1

Assumptions1. The equation $c=400w$ models the relationship between the number of weeks ( $w$ ) and the total number of copies of the newsletters printed ( $c$ ). . Each Friday, the school prints400 copies of the school newsletter.
3. The number of weeks ( $w$ ) is a whole number, as it's unlikely to consider a fraction of a week in this context.

STEP 2

The equation $c=400w$ is a linear equation in the form of $y=mx$ , where $m$ is the slope of the line. Here, $c$ is analogous to $y$ , $w$ is analogous to $x$ , and400 is the slope of the line.

STEP 3

The slope of the line,400, represents the rate at which the total number of copies of the newsletters ( $c$ ) increases for each week ( $w$ ). In other words, for each increase of1 in $w$ , $c$ increases by400.

STEP 4

A viable point on the graph is any point $(w, c)$ where $w$ is a whole number (representing the number of weeks) and $c$ is the corresponding number of newsletters printed, calculated as $c=400w$ .

STEP 5

To find a viable point, we can choose a value for $w$ and calculate the corresponding value of $c$ . For example, let's choose $w=1$ .

STEP 6

Substitute $w=1$ into the equation to find the corresponding value of $c$ .
$c =400 \times1$

STEP 7

Calculate the value of $c$ .
$c =400 \times1 =400$

STEP 8

So, a viable point on the graph is $(1,400)$ , which means that after1 week,400 newsletters have been printed.

STEP 9

The values of $w$ must be whole numbers (,,2,3, ...) because it's unlikely to consider a fraction of a week in this context. The values of $c$ are calculated as $c=400w$ and will be multiples of400.
The graph of this scenario is a straight line passing through the origin (,) and increasing at a rate of400 newsletters per week. The line will pass through points where the x-coordinate is a whole number and the y-coordinate is a multiple of400.

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QuestionEach Friday, 400 newsletters are printed. The equation $c=400 w$ relates weeks $w$ to total copies $c$ . What is true of the graph?

Studdy Solution

STEP 1

STEP 2

The equation $c=400w$ is a linear equation in the form of $y=mx$ , where $m$ is the slope of the line. Here, $c$ is analogous to $y$ , $w$ is analogous to $x$ , and400 is the slope of the line.

STEP 3

The slope of the line,400, represents the rate at which the total number of copies of the newsletters ( $c$ ) increases for each week ( $w$ ). In other words, for each increase of1 in $w$ , $c$ increases by400.

STEP 4

A viable point on the graph is any point $(w, c)$ where $w$ is a whole number (representing the number of weeks) and $c$ is the corresponding number of newsletters printed, calculated as $c=400w$ .

STEP 5

To find a viable point, we can choose a value for $w$ and calculate the corresponding value of $c$ . For example, let's choose $w=1$ .

STEP 6

Substitute $w=1$ into the equation to find the corresponding value of $c$ .
$c =400 \times1$

STEP 7

Calculate the value of $c$ .
$c =400 \times1 =400$

STEP 8

So, a viable point on the graph is $(1,400)$ , which means that after1 week,400 newsletters have been printed.

STEP 9

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QuestionEach Friday, 400 newsletters are printed. The equation c=400wc=400 wc=400w relates weeks www to total copies ccc. What is true of the graph?

Studdy Solution

STEP 1

STEP 2

The equation c=400wc=400wc=400w is a linear equation in the form of y=mxy=mxy=mx, where mmm is the slope of the line. Here, ccc is analogous to yyy, www is analogous to xxx, and400 is the slope of the line.

STEP 3

The slope of the line,400, represents the rate at which the total number of copies of the newsletters (ccc) increases for each week (www). In other words, for each increase of1 in www, ccc increases by400.

STEP 4

A viable point on the graph is any point (w,c)(w, c)(w,c) where www is a whole number (representing the number of weeks) and ccc is the corresponding number of newsletters printed, calculated as c=400wc=400wc=400w.

STEP 5

To find a viable point, we can choose a value for www and calculate the corresponding value of ccc. For example, let's choose w=1w=1w=1.

STEP 6

Substitute w=1w=1w=1 into the equation to find the corresponding value of ccc.c=400×1c =400 \times1c=400×1

STEP 7

Calculate the value of ccc.c=400×1=400c =400 \times1 =400c=400×1=400

STEP 8

So, a viable point on the graph is (1,400)(1,400)(1,400), which means that after1 week,400 newsletters have been printed.

STEP 9

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QuestionEach Friday, 400 newsletters are printed. The equation $c=400 w$ relates weeks $w$ to total copies $c$ . What is true of the graph?

The equation $c=400w$ is a linear equation in the form of $y=mx$ , where $m$ is the slope of the line. Here, $c$ is analogous to $y$ , $w$ is analogous to $x$ , and400 is the slope of the line.

The slope of the line,400, represents the rate at which the total number of copies of the newsletters ( $c$ ) increases for each week ( $w$ ). In other words, for each increase of1 in $w$ , $c$ increases by400.

A viable point on the graph is any point $(w, c)$ where $w$ is a whole number (representing the number of weeks) and $c$ is the corresponding number of newsletters printed, calculated as $c=400w$ .

To find a viable point, we can choose a value for $w$ and calculate the corresponding value of $c$ . For example, let's choose $w=1$ .

Substitute $w=1$ into the equation to find the corresponding value of $c$ .
$c =400 \times1$

Calculate the value of $c$ .
$c =400 \times1 =400$

So, a viable point on the graph is $(1,400)$ , which means that after1 week,400 newsletters have been printed.