2. Use the graph the answer the following questions.
(3 points)
a. The constant of proportionality is
30
.
b. Write an equation that represents this graph
y = x + 15
.
c. This is a proportional relationship because the y-intercept is
(0, 15)
a. The constant of proportionality is 1.
b. Write an equation that represents this graph y = 1x + 15.
c. This is not a proportional relationship because the y-intercept is (0, 15) and the y-intercept is not at (0,0).
To answer these questions, we need to analyze the given graph.
a. The constant of proportionality can be found by looking at the slope of the graph. In this case, the slope is 1. Since the constant of proportionality is equal to the slope, the constant of proportionality is 1.
b. To write an equation that represents the graph, we need to use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. From the graph, we can see that the slope is 1 and the y-intercept is 15. Therefore, the equation that represents this graph is y = x + 15.
c. A proportional relationship is a relationship where the ratio of y to x is constant. In this case, when x is 0, y is 15, which gives us the point (0, 15). This is the y-intercept of the graph, and since the ratio of y to x is constant (1), this relationship is considered proportional.
To answer these questions using the given graph, follow these steps:
a. The constant of proportionality is determined by finding the slope of the graph. The slope represents the rate at which y increases or decreases as x increases. In this case, we can see that for every 1 unit increase in x, y also increases by 1 unit. Therefore, the constant of proportionality is 1.
b. To write an equation that represents the graph, we need to consider the slope and the y-intercept. From the graph, we can observe that the line intersects the y-axis at 15. This y-intercept indicates that when x is 0, y equals 15. The slope, as determined in part a, is 1. Therefore, the equation that represents this graph is y = x + 15.
c. This is a proportional relationship because the equation y = x + 15 is in slope-intercept form (y = mx + b), where m represents the slope (in this case, the constant of proportionality) and b represents the y-intercept. Since the y-intercept is (0, 15), it means that when x is 0, y is equal to 15. This indicates a direct proportion, where the values of y are directly proportional to the values of x.