How to Graph a Proportional Relationship with Slope 0.4

TL;DR

To graph a proportional relationship with a unit rate of 0.4, start at the point (0,0) and plot points where y increases by 0.4 for each increase of 1 in x. The equation of the line is y = 0.4x, and the slope, representing the rate of change, is also 0.4.

Transcript

Graph the line that represents a proportional relationship between y and x with a unit rate 0.4. That is, a change of one unit in x corresponds to a change of 0.4 units in y. And they also ask us to figure out what the equation of this line actually is. So let me get my scratch pad out and we could think about it. So let's just think about some pot... Read More

Key Insights

• 🥳 Proportional relationships have a constant ratio between the variables involved.
• 😥 The point (0,0) is always on the graph of a proportional relationship.
• ☠️ The slope of the graph represents the rate of change between the variables.
• 🤩 The equation of a proportional relationship is of the form y = kx, where k is the constant of proportionality.
• 🇦🇪 Graphing a line with a unit rate requires identifying points where y increases by the unit rate as x increases by 1.
• 🏙️ The equation y = 0.4x represents a line with a proportional relationship and a unit rate of 0.4.
• 🫥 The slope of the graph determines the steepness or slope of the line.

Questions & Answers

Q: How do you determine if a relationship is proportional?

A proportional relationship can be identified if the equation is in the form y = kx, where k represents the constant of proportionality.

Q: What does the point (0,0) signify on the graph?

The point (0,0) indicates that when there are zero x-values, there will also be zero y-values. It is a fundamental property of proportional relationships.

Q: How can you find the slope of the graph?

The slope is determined by calculating the change in y divided by the change in x. In this case, the slope is 2/5 or 0.4.

Q: Why is the equation of the line y = 0.4x?

The equation of a proportional relationship is y = kx, where k is the constant of proportionality. In this case, the slope of 0.4 represents the value of k.

Summary & Key Takeaways

• To graph a proportional relationship, the point (0,0) should be on the line. As x increases by 1, y increases by 0.4.

• The point (5,2) is on the graph, indicating a change in x of 5 corresponds to a change in y of 2.

• The slope of the graph, representing the rate of change, is calculated to be 0.4. The equation of the line is y = 0.4x.