Which graph shows a proportional relationship in which the value of y is one-half of the value of x?
CLEAR SUBMIT
On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 2, 0) and the y-axis at (0, 2).
On a coordinate plane, a straight line with a positive slope goes through (negative 3, negative 6)crosses the x and y axis at (0, 0), and goes through (3, 6).
On a coordinate plane, a straight line with a positive slope goes through (negative 6, negative 3)crosses the x and y axis at (0, 0), and goes through (6, 3).
On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 2) and the x-axis at (2, 0).
The graph that shows a proportional relationship in which the value of y is one-half of the value of x is the last option: "On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 2) and the x-axis at (2, 0)."
The graph that shows a proportional relationship in which the value of y is one-half of the value of x is the third option: "On a coordinate plane, a straight line with a positive slope goes through (negative 6, negative 3) crosses the x and y-axis at (0, 0), and goes through (6, 3)."
To determine which graph shows a proportional relationship where the value of y is one-half of the value of x, we can analyze the given options.
In a proportional relationship, the ratio between the y-values and the x-values remains constant. Here, the ratio is 1:2, meaning that for every x-value, the corresponding y-value is one-half of that x-value.
Let's examine each graph and see if it meets this condition:
1. The straight line in option 1 crosses the x-axis at (-2, 0) and the y-axis at (0, 2). However, the ratio between these points is not 1:2, so this graph does not represent the given relationship.
2. The straight line in option 2 goes through (-3, -6), (0, 0), and (3, 6). This line satisfies the condition since for every x-value, the corresponding y-value is one-half of that x-value. Therefore, option 2 represents the proportional relationship.
3. The straight line in option 3 goes through (-6, -3), (0, 0), and (6, 3). Similar to option 2, this line also satisfies the condition and represents the proportional relationship.
4. The straight line in option 4 crosses the y-axis at (0, 2) and the x-axis at (2, 0). The ratio between these points is not 1:2, so this graph does not represent the given relationship.
Therefore, options 2 and 3 are the possible graphs that show a proportional relationship where the value of y is one-half of the value of x.