Use the image to answer the question.An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through five plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma 1 right parenthesis, left parenthesis 4 comma 2 right parenthesis, left parenthesis 6 comma 3 right parenthesis, and left parenthesis 8 comma 4 right parenthesis. The solid line forms the hypotenuse for two triangles. The first triangle is marked with a dotted line and has vertices with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma 0 right parenthesis, and left parenthesis 4 comma 2 right parenthesis. The base is labeled as 4, and the perpendicular height on the right is labeled as 2. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 4 comma 2 right parenthesis, left parenthesis 8 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis. The base is labeled as 4, and the perpendicular height on the right is labeled as 2.Use similar triangles to determine the slope of the line. Write your answer in fraction form.(1 point)The slope is .

Answer 1

To determine the slope of the line that passes through the points given, we can use the coordinates of two points located on the line.

The two points we can use are:

• Point A (0, 0)
• Point B (2, 1)

The slope (m) of a line is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (2, 1) \).

Substituting the values: \[ m = \frac{1 - 0}{2 - 0} = \frac{1}{2} \]

Now, let's also use another set of points:

• Point C (4, 2)
• Point D (6, 3)

Using the same slope formula: \[ m = \frac{3 - 2}{6 - 4} = \frac{1}{2} \]

Finally, we can check with the last set of points:

• Point E (8, 4)
• Point F (4, 2)

Using those points: \[ m = \frac{4 - 2}{8 - 4} = \frac{2}{4} = \frac{1}{2} \]

Since the slope remains consistent across all selected points, we can confirm that the slope of the line is:

\[ \text{The slope is } \frac{1}{2}. \]

Answer 2

Use the image to answer the question.

An illustration shows Quadrant 1 of a coordinate plane. The x-axis is labeled Ounces and ranges from 0 to 40 in 5 unit increments. The y-axis is labeled Cost in dollars and ranges from from 0.00 to 4.00 in increments of 0.50. The graph is titled Cost per Ounce. A line connects four points plotted on the graph. The coordinates of the plotted points are left parenthesis 0 comma 0 right parenthesis, left parenthesis 8 comma 0.80 right parenthesis, left parenthesis 15 comma 1.50 right parenthesis, and left parenthesis 30 comma 3.00 right parenthesis.

The graph displays the cost per ounce of canned peas. Use the graph to determine the unit rate of the proportional relationship.

(1 point)
Responses

Canned peas cost $30 per ounce.
Canned peas cost $30 per ounce.

Canned peas cost $10 per ounce.
Canned peas cost $10 per ounce.

Canned peas cost $3.00 per ounce.
Canned peas cost $3.00 per ounce.

Canned peas cost $0.10 per ounce.

Answer 3

To determine the unit rate of the proportional relationship from the graph, we can look at the cost per ounce based on the plotted points.

From the data provided, we can analyze the point that is relevant for finding the unit rate:

When the weight is 30 ounces, the cost is $3.00. To find the cost per ounce, we can calculate the unit rate as follows:

\[ \text{Unit Rate} = \frac{\text{Cost}}{\text{Ounces}} = \frac{3.00 \text{ dollars}}{30 \text{ ounces}} = 0.10 \text{ dollars per ounce} \]

Thus, the unit rate of the proportional relationship is:

Canned peas cost $0.10 per ounce.

Answer 4

Use the image to answer the question.

An illustration shows two graphs depicting cost of gasoline per gallon in dollars in store A and B. The first graph shows cost of gasoline per gallon in dollars in store A. The horizontal axis shows gallons ranging from 0 to 20 in increments of 5. The vertical axis shows the cost in dollars ranging from 0 to 70 in increments of 10. Four data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 5 comma 20 right parenthesis, left parenthesis 10 comma 40 right parenthesis, and left parenthesis 15 comma 60 right parenthesis. A line connects all the data points. The second graph shows cost of gasoline per gallon in dollars in store B. The horizontal axis shows gallons ranging from 0 to 10 in increments of 2. The vertical axis shows the cost in dollars ranging from 0 to 30 in increments of 2. Three data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma 14 right parenthesis, and left parenthesis 8 comma 28 right parenthesis. A line connects all the data points.

The proportional relationship between the cost of gasoline and the number of gallons of gasoline from Store A and Store B are displayed in the graphs. Use the graphs to interpret the store that has the cheaper cost of gasoline per gallon.

(1 point)
Responses

Store B has the cheaper gasoline. The cost of gasoline at Store A is $5 per gallon.
Store B has the cheaper gasoline. The cost of gasoline at Store A is $5 per gallon.

Store A has the cheaper gasoline. The cost of gasoline is $0.25 per gallon.
Store A has the cheaper gasoline. The cost of gasoline is $0.25 per gallon.

Store B has the cheaper gasoline. The cost of gasoline is $3.50 per gallon.
Store B has the cheaper gasoline. The cost of gasoline is $3.50 per gallon.

Store B has the cheaper gasoline. The cost of gasoline at Store A is $100 per gallon.

Answer 5

To determine which store has the cheaper cost of gasoline per gallon, we need to calculate the price per gallon for both Store A and Store B based on the data points provided.

For Store A:

The points are:

• (0, 0)
• (5, 20)
• (10, 40)
• (15, 60)

From these points, we can analyze the cost for the gallons provided.

1. At \(5\) gallons, the cost is \($20\): \[ \text{Cost per gallon} = \frac{20}{5} = $4 , \text{per gallon} \]

2. At \(10\) gallons, the cost is \($40\): \[ \text{Cost per gallon} = \frac{40}{10} = $4 , \text{per gallon} \]

3. At \(15\) gallons, the cost is \($60\): \[ \text{Cost per gallon} = \frac{60}{15} = $4 , \text{per gallon} \]

For Store B:

The points are:

• (0, 0)
• (4, 14)
• (8, 28)

Now calculating the cost for Store B:

1. At \(4\) gallons, the cost is \($14\): \[ \text{Cost per gallon} = \frac{14}{4} = $3.50 , \text{per gallon} \]

2. At \(8\) gallons, the cost is \($28\): \[ \text{Cost per gallon} = \frac{28}{8} = $3.50 , \text{per gallon} \]

Conclusion:

• The cost of gasoline at Store A is \($4.00\) per gallon.
• The cost of gasoline at Store B is \($3.50\) per gallon.

Thus, Store B has the cheaper gasoline.

Answer: Store B has the cheaper gasoline. The cost of gasoline at Store A is $4 per gallon.

(Note: The original options provided had some inconsistencies regarding the price. The calculated price for Store A is consistently $4 per gallon based on the data points shared.)

Answer 6

Use the image to answer the question.An illustration shows two graphs depicting points per game for players A and B. The first graph shows points per game for player A. The horizontal axis shows games ranging from 0 to 5 in increments of 1. The vertical axis shows points ranging from 0 to 85 in increments of 5. Three data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma 40 right parenthesis, and left parenthesis 4 comma 80 right parenthesis. A line connects all the data points. The second graph shows points per game for player B. The horizontal axis shows games ranging from 0 to 6 in increments of 1. The vertical axis shows points ranging from 0 to 80 in increments of 5. Three data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 3 comma 45 right parenthesis, and left parenthesis 5 comma 75 right parenthesis. A line connects all the data points.The average points scored playing basketball for Player A and Player B are graphed in the graphs. Determine which player averaged more points per game.(1 point)ResponsesPlayer A averaged more points than Player B. Player A averaged 80 points per game.Player A averaged more points than Player B. Player A averaged 80 points per game.Player B averaged more points than Player A. Player B averaged 45 points per game.Player B averaged more points than Player A. Player B averaged 45 points per game.Player A averaged more points than Player B. Player A averaged 20 points per game.Player A averaged more points than Player B. Player A averaged 20 points per game.Player B averaged more points than Player A. Player B averaged 75 points per game. Player B averaged more points than Player A. Player B averaged 75 points per game.

Answer 7

To determine which player averaged more points per game, we can analyze the data points given for both players:

For Player A:

• The plotted points are:
  • (0, 0)
  • (2, 40)
  • (4, 80)

From this, notice that:

• At 0 games, the average is 0 points.
• At 2 games, the average is 40 points.
• At 4 games, the average is 80 points.

The highest average points scored by Player A is 80 points per game at 4 games.

For Player B:

• The plotted points are:
  • (0, 0)
  • (3, 45)
  • (5, 75)

From this, we see:

• At 0 games, the average is 0 points.
• At 3 games, the average is 45 points.
• At 5 games, the average is 75 points.

The highest average points scored by Player B is 75 points per game at 5 games.

Conclusion:

Comparing the highest averages:

• Player A averages 80 points per game.
• Player B averages 75 points per game.

Thus, Player A averaged more points than Player B. Player A averaged 80 points per game.

Answer 8

Use the image to answer the question.An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through two plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. Explain why the slope is positive or negative.(1 point)ResponsesThe slope is positive because the line increases as you move from left to right on the graph.The slope is positive because the line increases as you move from left to right on the graph.The slope is negative because the line decreases as you move from left to right on the graph.The slope is negative because the line decreases as you move from left to right on the graph.The slope is positive because the line decreases as you move from left to right on the graph.The slope is positive because the line decreases as you move from left to right on the graph.The slope is negative because the line increases as you move from left to right on the graph.

Answer 9

To determine why the slope of the line is positive, we need to look at how the line behaves as we move along the x-axis from left to right.

The line passes through the points (0, 0) and (6, 6).

• When you move from the point (0, 0) to (6, 6), the y-coordinate increases from 0 to 6 while the x-coordinate increases from 0 to 6 as well.

Because both the x and y values are increasing in this interval, the line is going upwards as you move from left to right on the graph.

Conclusion:

The slope is positive because the line increases as you move from left to right on the graph.

Correct response: The slope is positive because the line increases as you move from left to right on the graph.

Answer 10

Use the image to answer the question.An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through four plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma negative 2 right parenthesis, left parenthesis 4 comma negative 4 right parenthesis, and left parenthesis 6 comma negative 6 right parenthesis. The solid line forms the hypotenuse for two triangles. The first triangle is marked with a dotted line and has vertices with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 2 right parenthesis. The base is labeled as 2, and the perpendicular height on the left is labeled as 2. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 2 comma negative 2 right parenthesis, left parenthesis 2 comma negative 6 right parenthesis, and left parenthesis 6 comma negative 6 right parenthesis. The base is labeled as 4, and the perpendicular height on the left is labeled as 4.What is the slope of the line?(1 point)Responses11−1negative 1−2negative 222Skip to navigation

Answer 11

To calculate the slope of the line that passes through the given points, we can use the formula for slope:

\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's use two of the points provided on the line: \( (0, 0) \) and \( (6, -6) \).

Substituting these points into the slope formula:

• \( (x_1, y_1) = (0, 0) \)
• \( (x_2, y_2) = (6, -6) \)

The calculation will be:

\[ m = \frac{-6 - 0}{6 - 0} = \frac{-6}{6} = -1 \]

Thus, the slope of the line is \(-1\).

Final Answer: The slope of the line is \(-1\).