Identify proportional relationships by graphing
Key Notes:
The graph of a proportional relationship between x and y is a straight line passing through the origin, (0,0).
Learn with an example
đ„As a young girl, Evelyn enjoyed watching her father make things in his woodworking shop. Now that she’s grown up, Evelyn builds wooden furniture for a living. Her most popular product is a cedar porch swing. It takes Evelyn 3 days to build 1 swing. It takes her 9 days to build 3 swings.
In this relationship, x represents the time (in days) Evelyn spends making porch swings, and y represents the number of swings she builds.
Graph two points for this relationship and the line passing through them.

According to the graph, do x and y have a proportional relationship?
yes______
no______
To find two points for this relationship, look for clues in the problem related to x-and y-values.
As a young girl, Evelyn enjoyed watching her father make things in his woodworking shop. Now that she’s grown up, Evelyn builds wooden furniture for a living. Her most popular product is a cedar porch swing. It takes Evelyn 3 days to build 1 swing.It takes her 9 days to build 3 swings.
In this relationship, x represents the time (in days) Evelyn spends making porch swings, and y represents the number of swings she builds
The problem describes the points (3, 1) and (9, 3). Plot these points on the graph.

To determine whether x and y have a proportional relationship, see if the line through these points passes through the origin, (0, 0).

The points are on a line that passes through the origin. So, x and y have a proportional relationship.
đ„Every day after school, Quinn and his sister Layla play their favorite video game, Wizarding Legends. The goal of the game is to earn power points by defeating goblins. Today, Quinn defeated 2 goblins and earned 4 power points. Layla defeats 5 goblins and earns 10 power points.
In this relationship, x represents the number of goblins defeated, and y represents the number of power points earned.
Graph two points for this relationship and the line passing through them.

According to the graph, do x and y have a proportional relationship?
yes_____
no_____
To find two points for this relationship, look for clues in the problem related to x– and y-values.
Every day after school, Quinn and his sister Layla play their favorite video game, Wizarding Legends. The goal of the game is to earn power points by defeating goblins. Today, Quinn defeats 2 goblins and earned 4 power points. Layla defeats 5 goblins and earns 10 power points.
In this relationship, x represents the number of goblins defeated, and y represents the number of power points earned.
The problem describes the points (2, 4) and (5, 10). Plot these points on the graph.

To determine whether x and y have a proportional relationship, see if the line through these points passes through the origin, (0, 0).

The points are on a line that passes through the origin. So, x and y have a proportional relationship.
đ„Harvey has outgrown the bike he rode when he was small. So, for his twelfth birthday, his parents surprised him with a five-speed Blaze Rider 2000! Harvey has never had a bike with multiple speeds before, and he is eager to learn how it works. He starts by testing the middle speed. When he pedals 1 time, the wheels rotate 1 time. When he pedals 10 times, the wheels rotate 10 times.
In this relationship, x represents the number of times Harvey pedals, and y represents the number of times the wheels rotate.
Graph two points for this relationship and the line passing through them.

According to the graph, do x and y have a proportional relationship?
yes______
no______
To find two points for this relationship, look for clues in the problem related to x– and y-values.
Harvey has outgrown the bike he rode when he was small. So, for his twelfth birthday, his parents surprise him with a five-speed Blaze Rider 2000! Harvey has never had a bike with multiple speeds before, and he is eager to learn how it works. He starts by testing the middle speed. When he pedals 1 time, the wheels rotate 1 time. When he pedals 10 times, the wheels rotate 10 times.
In this relationship, x represents the number of times Harvey pedals, and y represents the number of times the wheels rotate.
The problem describes the points (1, 1) and (10, 10). Plot these points on the graph.

To determine whether x and y have a proportional relationship, see if the line through these points passes through the origin, (0, 0).

The points are on a line that passes through the origin. So, x and y have a proportional relationship.
let’s practice!