Graph the line that passes through the coordinates below and determine which statement is true.
(2,3), (3,4.5), (4,6), (6,9)
A.
The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
B.
The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin.
C.
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
D.
The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
To determine which statement is true, we can graph the line passing through the given coordinates.
First, let's plot the coordinates (2,3), (3,4.5), (4,6), and (6,9) on a graph:
(2,3) is represented by the point A
(3,4.5) is represented by the point B
(4,6) is represented by the point C
(6,9) is represented by the point D
Now, we can connect these points to form a line:
D
/
/
/
A-----B-----C
Looking at the graph, we can see that the line does not pass through the origin (0,0). Therefore, we can conclude that the statement C is true:
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
So, the correct answer is C.
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
To determine if the line represents a proportional relationship, we can use the slope formula.
The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:
m = (y2 - y1) / (x2 - x1)
Using the given coordinates (2,3) and (3,4.5):
m = (4.5 - 3) / (3 - 2)
= 1.5 / 1
= 1.5
The slope is 1.5.
To determine if the line passes through the origin, we can substitute one of the given points (2,3) into the equation y = mx + b, where b is the y-intercept.
3 = 1.5(2) + b
3 = 3 + b
b = 0
The y-intercept (b) is 0, indicating that the line passes through the origin.
Since the line does not pass through the origin, the correct statement is: The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
Answer: C.
To determine which statement is true, we can start by graphing the line that passes through the given coordinates. Here are the steps to graph a line:
1. First plot the given points on a coordinate plane. For this question, we have the following points:
(2,3), (3,4.5), (4,6), (6,9)
2. Connect the points with a straight line. This line represents the relationship between the points.
After plotting the points and connecting them with a line, we can look at the graph to determine which statement is true.
If the line passes through the origin (0,0), it represents a proportional relationship. This is because a proportional relationship means that the dependent variable (y) is directly proportional to the independent variable (x), and passes through the origin.
If the line does not pass through the origin, it does not represent a proportional relationship.
Now, let's analyze the graphed line:
Looking at the graph, we can observe that the line does not pass through the origin (0,0). Therefore, we can eliminate statements A and B.
Statement C says that the line does not represent a proportional relationship because it does not pass through the origin. Since the line does not pass through the origin, this statement is true.
Statement D says that the line represents a proportional relationship because it does not pass through the origin. Since the line does not pass through the origin, this statement is false.
Therefore, the correct answer is C. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.