Mathematics
Grade 7
15 min
Write an equation from a graph using a table
Write an equation from a graph using a table
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1
Introduction & Learning Objectives
Learning Objectives
Identify ordered pairs (x, y) from a given graph.
Organize selected ordered pairs from a graph into a table of values.
Determine the constant of proportionality (k) by analyzing the relationship between x and y in a table.
Write a two-variable equation in the form y = kx that represents the relationship shown in the table and graph.
Verify the written equation by substituting additional points from the graph.
Explain the meaning of the constant of proportionality in the context of a given problem.
Have you ever seen a graph and wondered if there was a secret math rule behind it? 🕵️♀️ What if you could turn a picture into an equation?
In this lesson, you'll learn how to take information from a visual graph, organize it into a table, and then discove...
2
Key Concepts & Vocabulary
TermDefinitionExample
GraphA visual representation of data, often showing the relationship between two variables on a coordinate plane.A line drawn on a grid with an x-axis and a y-axis.
Ordered PairA pair of numbers (x, y) that represents a point's location on a coordinate plane, where x is the horizontal position and y is the vertical position.(2, 4) means 2 units right from the origin and 4 units up.
Table of ValuesAn organized list that shows the relationship between two variables, typically x and y, by listing corresponding ordered pairs.A table with columns for 'x' and 'y' and rows for each (x,y) pair.
Two-variable EquationAn equation that contains two different variables, usually x and y, and shows how they are related.y = 2x or y = x + 5
Constant of Propor...
3
Core Formulas
Rule for Finding the Constant of Proportionality
$$k = \frac{y}{x}$$
To find the constant of proportionality (k) in a proportional relationship, divide the y-value by its corresponding x-value for any point (x, y) on the graph (except the origin).
Equation for Proportional Relationships
$$y = kx$$
Once the constant of proportionality (k) is found, this equation can be used to represent the relationship between x and y for all points on the graph that show a direct variation (a straight line through the origin).
Identifying Proportional Relationships from a Graph
A relationship is proportional if its graph is a straight line that passes through the origin (0,0).
Before trying to find 'k' and write 'y=kx', always check if the graph is a straight lin...
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Challenging
A graph shows the cost of downloading songs. A student creates a table with points (2 songs, $2.50) and (4 songs, $5.00). They correctly write the equation y = 1.25x. In the context of this problem, what does the point (1, 1.25) represent?
A.The total cost of 1.25 songs.
B.The cost for one song, which is the unit rate.
C.The time it takes to download one song.
D.point that is not on the graph.
Challenging
A graph shows a straight line passing through the points (2, 5) and (4, 9). A student creates a table with these points. Why can't they write a correct equation for this line in the form y = kx?
A.Because the line uses points with even numbers.
B.Because the line does not pass through the origin (0, 0).
C.Because the y-values are greater than the x-values.
D.Because it is impossible to find the relationship between x and y.
Challenging
A graph represents the amount of sugar (y, in cups) needed for a cookie recipe based on the number of dozens of cookies (x). The line is proportional and passes through (4, 6). Using the equation derived from the graph, what is the maximum number of full dozens of cookies that can be made with 20 cups of sugar?
A.12 dozens
B.14 dozens
C.30 dozens
D.13 dozens
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