Solved on Feb 12, 2024

The fire department has 240 stickers to distribute in bags, some with 3 stickers and some with 4 stickers. The equation $3x + 4y = 240$ represents this relationship. The graph of this equation is a line through the points $(60,0)$ and $(0,80)$ .

STEP 1

Assumptions
1. The equation representing the relationship between the number of bags with 3 stickers ( $x$ ) and the number of bags with 4 stickers ( $y$ ) is $3x + 4y = 240$ .
2. We are looking for points on the graph of this equation where either $x=0$ or $y=0$ .

STEP 2

First, we will find the point on the graph where $y=0$ . This will give us the $x$ -intercept, which is the point where the line crosses the $x$ -axis.
$3x + 4(0) = 240$

STEP 3

Solve the equation for $x$ when $y=0$ .
$3x = 240$

STEP 4

Divide both sides of the equation by 3 to solve for $x$ .
$x = \frac{240}{3}$

STEP 5

Calculate the value of $x$ .
$x = 80$

STEP 6

Now we have the $x$ -intercept, which is the point $(80, 0)$ .

STEP 7

Next, we will find the point on the graph where $x=0$ . This will give us the $y$ -intercept, which is the point where the line crosses the $y$ -axis.
$3(0) + 4y = 240$

STEP 8

Solve the equation for $y$ when $x=0$ .
$4y = 240$

STEP 9

Divide both sides of the equation by 4 to solve for $y$ .
$y = \frac{240}{4}$

STEP 10

Calculate the value of $y$ .
$y = 60$

STEP 11

Now we have the $y$ -intercept, which is the point $(0, 60)$ .

STEP 12

We have found the two intercepts of the line represented by the equation $3x + 4y = 240$ . These points are $(80, 0)$ and $(0, 60)$ . The graph is a line that goes through these points.
The correct statement about the graph of the relationship is: The graph is a line that goes through the points $(80,0)$ and $(0,60)$ .

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The fire department has 240 stickers to distribute in bags, some with 3 stickers and some with 4 stickers. The equation $3x + 4y = 240$ represents this relationship. The graph of this equation is a line through the points $(60,0)$ and $(0,80)$ .

STEP 1

Assumptions
1. The equation representing the relationship between the number of bags with 3 stickers ( $x$ ) and the number of bags with 4 stickers ( $y$ ) is $3x + 4y = 240$ .
2. We are looking for points on the graph of this equation where either $x=0$ or $y=0$ .

STEP 2

First, we will find the point on the graph where $y=0$ . This will give us the $x$ -intercept, which is the point where the line crosses the $x$ -axis.
$3x + 4(0) = 240$

STEP 3

Solve the equation for $x$ when $y=0$ .
$3x = 240$

STEP 4

Divide both sides of the equation by 3 to solve for $x$ .
$x = \frac{240}{3}$

STEP 5

Calculate the value of $x$ .
$x = 80$

STEP 6

Now we have the $x$ -intercept, which is the point $(80, 0)$ .

STEP 7

Next, we will find the point on the graph where $x=0$ . This will give us the $y$ -intercept, which is the point where the line crosses the $y$ -axis.
$3(0) + 4y = 240$

STEP 8

Solve the equation for $y$ when $x=0$ .
$4y = 240$

STEP 9

Divide both sides of the equation by 4 to solve for $y$ .
$y = \frac{240}{4}$

STEP 10

Calculate the value of $y$ .
$y = 60$

STEP 11

Now we have the $y$ -intercept, which is the point $(0, 60)$ .

STEP 12

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The fire department has 240 stickers to distribute in bags, some with 3 stickers and some with 4 stickers. The equation 3x+4y=2403x + 4y = 2403x+4y=240 represents this relationship. The graph of this equation is a line through the points (60,0)(60,0)(60,0) and (0,80)(0,80)(0,80).

STEP 1

Assumptions1. The equation representing the relationship between the number of bags with 3 stickers (xxx) and the number of bags with 4 stickers (yyy) is 3x+4y=2403x + 4y = 2403x+4y=240.2. We are looking for points on the graph of this equation where either x=0x=0x=0 or y=0y=0y=0.

STEP 2

First, we will find the point on the graph where y=0y=0y=0. This will give us the xxx-intercept, which is the point where the line crosses the xxx-axis.3x+4(0)=2403x + 4(0) = 2403x+4(0)=240

STEP 3

Solve the equation for xxx when y=0y=0y=0.3x=2403x = 2403x=240

STEP 4

Divide both sides of the equation by 3 to solve for xxx.x=2403x = \frac{240}{3}x=3240​

STEP 5

Calculate the value of xxx.x=80x = 80x=80

STEP 6

Now we have the xxx-intercept, which is the point (80,0)(80, 0)(80,0).

STEP 7

Next, we will find the point on the graph where x=0x=0x=0. This will give us the yyy-intercept, which is the point where the line crosses the yyy-axis.3(0)+4y=2403(0) + 4y = 2403(0)+4y=240

STEP 8

Solve the equation for yyy when x=0x=0x=0.4y=2404y = 2404y=240

STEP 9

Divide both sides of the equation by 4 to solve for yyy.y=2404y = \frac{240}{4}y=4240​

STEP 10

Calculate the value of yyy.y=60y = 60y=60

STEP 11

Now we have the yyy-intercept, which is the point (0,60)(0, 60)(0,60).

STEP 12

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The fire department has 240 stickers to distribute in bags, some with 3 stickers and some with 4 stickers. The equation $3x + 4y = 240$ represents this relationship. The graph of this equation is a line through the points $(60,0)$ and $(0,80)$ .

Assumptions
1. The equation representing the relationship between the number of bags with 3 stickers ( $x$ ) and the number of bags with 4 stickers ( $y$ ) is $3x + 4y = 240$ .
2. We are looking for points on the graph of this equation where either $x=0$ or $y=0$ .

First, we will find the point on the graph where $y=0$ . This will give us the $x$ -intercept, which is the point where the line crosses the $x$ -axis.
$3x + 4(0) = 240$

Solve the equation for $x$ when $y=0$ .
$3x = 240$

Divide both sides of the equation by 3 to solve for $x$ .
$x = \frac{240}{3}$

Calculate the value of $x$ .
$x = 80$

Now we have the $x$ -intercept, which is the point $(80, 0)$ .

Next, we will find the point on the graph where $x=0$ . This will give us the $y$ -intercept, which is the point where the line crosses the $y$ -axis.
$3(0) + 4y = 240$

Solve the equation for $y$ when $x=0$ .
$4y = 240$

Divide both sides of the equation by 4 to solve for $y$ .
$y = \frac{240}{4}$

Calculate the value of $y$ .
$y = 60$

Now we have the $y$ -intercept, which is the point $(0, 60)$ .