2. Use the graph the answer the following questions.
(3 points)
a. The constant of proportionality is
.
b. Write an equation that represents this graph
.
c. This is a proportional relationship because the y-intercept is
.
a. The constant of proportionality is the slope of the graph. By looking at the graph, we can determine that the slope is 1/2.
b. The equation that represents this graph can be written as y = (1/2)x.
c. This is a proportional relationship because the y-intercept is 0. In a proportional relationship, the y-intercept is always 0.
To answer the questions, I would need to see the graph you are referring to. Please provide the graph so I can assist you further.
To answer these questions, we need to analyze the graph and identify its characteristics.
a. The constant of proportionality can be found by examining the slope of the line on the graph. The slope represents the ratio of the change in the y-values to the change in the x-values. For a proportional relationship, the ratio should remain constant throughout.
In this case, find two points on the line and calculate the ratio of the change in y to the change in x. For instance, if we take two points (-2, -4) and (2, 4), the change in y is 4 - (-4) = 8 and the change in x is 2 - (-2) = 4. Therefore, the constant of proportionality is 8/4 = 2.
b. To write an equation that represents this graph, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
From the graph, we can observe that the line intersects the y-axis at (0, 0). This means that the y-intercept, b, is 0. The slope, identified in part a as 2, can be used as the coefficient of x.
Thus, the equation representing this graph is y = 2x.
c. To determine if this is a proportional relationship, we need to check the y-intercept. In this case, as observed in part b, the y-intercept is 0. If the y-intercept is 0, we can conclude that the relationship is proportional.