Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Which of these objects is moving at a rate of 2 feet per second?
(1 point)
Responses
all of the objects
all of the objects
object A
object A
object C
object C
object B
object B
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled total cost in dollars and the x-axis is titled number of markers. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Predict what the total cost would be for buying 10 of the type A markers.
(1 point)
Responses
$0.50
$0.50
$20.00
$20.00
$5.00
$5.00
$2.00
$5.00
To determine which object is moving at a rate of 2 feet per second, we need to consider the slope of the lines. The slope of a line represents the rate of change between two points.
The slope formula is:
slope = (change in y) / (change in x)
Let's apply this formula to the given lines:
Object A:
The line passes through the points (0, 0) and (3, 6).
The change in y = 6 - 0 = 6
The change in x = 3 - 0 = 3
slope = (6 - 0) / (3 - 0) = 6 / 3 = 2
Therefore, the slope of object A is 2, which means it is moving at a rate of 2 feet per second.
Object B:
The line passes through the points (0, 0) and (6, 6).
The change in y = 6 - 0 = 6
The change in x = 6 - 0 = 6
slope = (6 - 0) / (6 - 0) = 6 / 6 = 1
Therefore, the slope of object B is 1, not 2.
Object C:
The line passes through the points (0, 0) and (6, 3).
The change in y = 3 - 0 = 3
The change in x = 6 - 0 = 6
slope = (3 - 0) / (6 - 0) = 3 / 6 = 0.5
Therefore, the slope of object C is 0.5, not 2.
Therefore, the only object moving at a rate of 2 feet per second is object A.