a. The constant of proportionality is
b. Write an equation that represents the linear graph. Response area
c. This is a proportional relationship because the graph shows
a. The constant of proportionality is a number that relates the variables in a proportional relationship. It represents the rate of change or ratio between the two variables. It can be found by dividing the change in the dependent variable (y) by the change in the independent variable (x).
b. The equation that represents the linear graph in a proportional relationship is y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality.
c. This is a proportional relationship because the graph shows a straight line passing through the origin (0,0). It indicates that for every increase or decrease in the independent variable, the dependent variable changes in a consistent and proportional manner.
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a. The constant of proportionality can be determined by taking the ratio of any two pairs of corresponding values on the graph. Choose two points on the graph, let's say (x1, y1) and (x2, y2), with x1 ≠ x2. The constant of proportionality is given by:
constant of proportionality = (y2 - y1) / (x2 - x1)
b. To write an equation that represents the linear graph, we can use the slope-intercept form of a linear equation, which is y = mx + b.
We already know the constant of proportionality is the slope (m) of the graph. Choose any point on the graph, let's say (x1, y1), and substitute the values into the equation:
y1 = m(x1) + b
This equation represents the linear graph.
c. This is a proportional relationship because the graph shows a straight line passing through the origin (0, 0). This implies that as the input variable (x) increases or decreases, the output variable (y) also increases or decreases at a constant rate, indicating proportionality.
a. To find the constant of proportionality, you need two pieces of information: a specific point on the graph and the corresponding values for the independent and dependent variables. Let's assume we have a point (x, y) on the graph.
The constant of proportionality, often denoted as k or m, represents the ratio between the dependent variable (y) and the independent variable (x). It is calculated by dividing the value of the dependent variable by the value of the independent variable at the given point:
k = y / x
b. To write an equation that represents the linear graph, we need to determine the slope (m) and the y-intercept (b) of the line. The slope is the constant of proportionality, and the y-intercept is the point where the line crosses the y-axis.
The slope (m) can be found using the constant of proportionality (k) we calculated in part (a):
m = k
The y-intercept (b) can be found by identifying the point where the line crosses the y-axis (the value of y when x equals zero).
Once we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form (y = mx + b).
c. A graph represents a proportional relationship if it is a straight line that passes through the origin (0,0), or if all the points fall on a straight line that has a constant slope. In this case, if the graph meets either of these criteria, we can consider it a proportional relationship.