The constant of proportionality is a linear relationship
b. Write an equation that represents the linear graph. 5y = x
c. This is a proportional relationship because the graph shows linear with a y-intercept at (0, 0) .
b. The equation that represents the linear graph is y = (1/5)x.
c. This is a proportional relationship because the graph shows a linear relationship with a y-intercept at (0, 0), indicating that as x increases, y also increases at a constant rate.
To determine if a relationship is proportional, we look for a constant ratio between the two variables. In a linear relationship, the constant of proportionality corresponds to the slope of the line.
b. The equation given, 5y = x, represents a linear relationship. This equation can be rewritten in slope-intercept form (y = mx + b) by dividing both sides by 5: y = (1/5)x + 0. This equation implies that the slope (m) is 1/5, indicating a constant ratio between x and y.
c. The graph of the equation y = (1/5)x + 0 represents a linear relationship with a y-intercept at (0, 0). The fact that the line passes through the origin (0, 0) is indicative of a proportional relationship.