Mathematics
Grade 7
15 min
Interpret a graph: word problems
Interpret a graph: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify independent and dependent variables from a word problem and locate them on a graph.
Accurately read and interpret ordered pairs on a coordinate plane in the context of a word problem.
Calculate and interpret the slope (rate of change) of a linear graph from a word problem.
Identify and interpret the y-intercept of a linear graph in the context of a real-world scenario.
Answer specific questions by extracting information directly from a given graph.
Use a graph to make predictions or estimations related to the word problem.
Explain the meaning of different parts of a graph (points, lines, axes) in the context of a given word problem.
Ever wonder how scientists predict weather or how much money you'll save over time? 📈 Graphs are powerful t...
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Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA two-dimensional surface formed by the intersection of two perpendicular number lines, called axes. It's used to plot points.Imagine a city map where streets run north-south and east-west; you can find any location using two numbers.
Ordered PairA pair of numbers $(x, y)$ that represents a specific point on the coordinate plane. The first number (x) is the horizontal position, and the second number (y) is the vertical position.The point $(3, 5)$ means you move 3 units right from the origin and 5 units up.
Independent VariableThe variable whose value does not depend on another variable. It's usually plotted on the horizontal (x) axis.In a graph showing distance traveled over time, 'time' is the independent variable because distance...
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Core Formulas
Identifying Variables on a Graph
The horizontal axis (x-axis) typically represents the independent variable, and the vertical axis (y-axis) typically represents the dependent variable.
When interpreting a graph from a word problem, first identify what each axis represents. The units on the axes are crucial for understanding the context.
Interpreting an Ordered Pair
An ordered pair $(x, y)$ on a graph means that when the independent variable has a value of $x$, the dependent variable has a value of $y$.
To understand a specific point, relate its x-coordinate to the independent variable and its y-coordinate to the dependent variable, including their units.
Calculating and Interpreting Slope (Rate of Change)
The slope $m$ of a linear graph can be calculated using two poin...
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Challenging
A 1,000-gallon water tank drains completely in 5 hours at a constant rate. The graph of this situation starts at (0, 1000) and ends at (5, 0). Which equation represents the volume of water V in the tank after t hours?
A.V = 1000 - 200t
B.V = 1000 + 200t
C.V = 200t
D.V = 5 - 1000t
Challenging
A graph shows a bike ride. The x-axis is 'Time (hours)' and the y-axis is 'Distance from Start (km)'. The graph is a straight line from (0,0) to (1,15), then a horizontal line from (1,15) to (2,15), then a straight line from (2,15) to (3,30). What happened between hour 1 and hour 2?
A.The cyclist rode downhill very fast.
B.The cyclist took a 1-hour break.
C.The cyclist turned around and went back home.
D.The cyclist's speed increased.
Challenging
A graph shows the growth of a beanstalk. The x-axis is 'Time (days)' and the y-axis is 'Height (cm)'. The line passes through (0, 2) and (5, 17). Which of the following statements is the best interpretation of the data?
A.The beanstalk grows 17 cm every 5 days.
B.The beanstalk was planted 2 days before measurements started.
C.The beanstalk started at a height of 2 cm and grows at a rate of 3 cm per day.
D.After 10 days, the beanstalk will be 32 cm tall.
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