Homework 12/4

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant.

Front

What does the equation y = kx represent?

Back

This equation represents a proportional relationship where k is the constant of proportionality.

Front

How can you determine if two equations represent the same proportional relationship?

Back

You can compare the constants of proportionality (k) in both equations. If they are equal, the relationships are the same.

Front

What is the constant of proportionality in the equation y = 82x?

Back

The constant of proportionality is 82.

Front

If Restaurant S serves 82 people for each day it is open, how many people will it serve in 5 days?

Back

y = 82 * 5 = 410 people.

Front

What does it mean if two quantities are directly proportional?

Back

It means that as one quantity increases, the other quantity increases at a constant rate.

Front

Identify the decoy equation that does not represent a proportional relationship: y = 5x - 7.

Back

The equation y = 5x - 7 is not proportional because it has a constant term (-7) that shifts the line.

Front

What is the significance of the slope in a proportional relationship?

Back

The slope represents the constant of proportionality and indicates how much one quantity changes in relation to another.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the formula to convert a proportional relationship into a graph?

Back

Plot the points (x, y) where y = kx, and draw a straight line through the origin.