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 value that relates the independent variable to the dependent variable in a proportional relationship.
b. Write an equation that represents this graph: It would be in the form y = kx, where k is the constant of proportionality and x is the independent variable.
c. This is a proportional relationship because the y-intercept is 0. In a proportional relationship, the y-intercept is always 0.
a. The constant of proportionality is represented by the letter "k" or "m". It is a number that relates the values of two variables in a proportional relationship.
b. To write an equation that represents a proportional relationship, you can use the formula y = kx, where "y" represents the dependent variable, "x" represents the independent variable, and "k" represents the constant of proportionality.
c. In a proportional relationship, the y-intercept is always 0, since the relationship passes through the origin (0, 0). Therefore, the y-intercept is 0.
a. To determine the constant of proportionality, you need to look for a pattern in the relationship between two variables. If the relationship is proportional, then the ratio of the two variables will always be the same. The constant of proportionality is the value that relates the two variables. To find it, you can choose any two points on the graph and calculate the ratio of the corresponding y-values to x-values. The constant of proportionality is the same for any two points on the graph.
b. To write an equation that represents the graph, you can use the formula for a proportional relationship:
y = kx
where y is the dependent variable, x is the independent variable, and k is the constant of proportionality. You can substitute the value of the constant of proportionality found in part a into this equation.
c. In a proportional relationship, the y-intercept is always zero. This means that when the x-value is zero, the y-value will also be zero. If the y-intercept is not zero, then the relationship is not proportional.