We want to write an equation to model the given proportional relationship. We know that the equation for a proportional relationship is y=mx, where m represents the slope of the line. Therefore to write the equation, we need to find the slope of the given line. We can find it using any two points from the line.
We can see that the line passes through the points (2,24) and (6,72). As the graph travels from left to right, the rise — or change in y — is 48. Similarly, the run — or change in x — is 4.
Slope m is the ratio of the rise to the run. Let's find its value!
m=rise/run ⇒ m=48/4= 12
Slope is equal to 12. Now we can write an equation modeling the proportional relationship.
y= mx ⇔ y= 12x
We want to know how to recognize if an equation or a graph represents a proportional relationship.
Equation
The equation of a proportional relationship is y=mx, where m represents the slope of the line.
Therefore, when the equation is in the following form, we know that it represents a proportional relationship.
y = any number * x
Let's look at some examples!
Proportional Relationship
Not a Proportional Relationship
y= 2x
y=2x+3
y= sqrt(3)x
y=5x^2
y= - 7.5 x
y=x-10
Graph
A straight line represents a relationship between two variables that are proportional. Let's look at the graphs of a few proportional relationships.
These graphs are all straight lines that pass through the point (0,0), which is the origin of a coordinate plane. Therefore when the graph is a straight line and passes through the origin — we know that it represents a proportional relationship.
