Proportional Relationships for Kids: Tables, Graphs and y = kx (Grade 7 Math)

Hi, I'm Luna from DoodleBeez. Today we are learning about proportional relationships. Two amounts are proportional when one is always the same number times the other. That number is called the constant of proportionality.

Strawberries cost five dollars per box. Two boxes cost ten dollars, four boxes cost twenty, and six boxes cost thirty. Divide each y by its x. Every time we get five, so k is five.

Once we know k, we can write the equation. The cost is five times the number of boxes, so y equals five x. For ten boxes, the cost is five times ten, which is fifty dollars.

Not every table is proportional. Here, x is one, two and three, and y is four, six and eight. Four divided by one is four, but six divided by two is three. The answers are different, so it is not proportional.

On a graph, a proportional relationship is a straight line that goes through the origin, the point zero comma zero. Find the point where x is one. Its y value is the unit rate, which is k.

Proportional relationships are all around us. If you earn twelve dollars per hour, your pay is twelve times the hours. Zero hours gives zero dollars, and the pay grows by the same amount every hour.

Now it's your turn. When x is three, five and eight, y is twelve, twenty and thirty two. What is k, and what is the equation? Pause and try. Every y divided by x is four, so k is four and y equals four x.

Great job! Remember, y divided by x is always the same number, k. The equation is y equals k x, and the graph is a straight line through the origin. Practice proportional relationships in Middle School Math at doodlebeez.com. See you next time!