Mathematics
Grade 8
15 min
Complete a table and graph a linear function
Complete a table and graph a linear function
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1
Introduction & Learning Objectives
Learning Objectives
Identify the components of a linear function.
Evaluate a linear function for given input values to complete a table of values.
Accurately plot ordered pairs from a table onto a coordinate plane.
Draw a straight line through plotted points to represent a linear function.
Understand the relationship between an equation, a table of values, and its graph.
Use a graph to estimate output values for given input values.
Have you ever wondered how scientists predict the path of a rocket 🚀 or how a company calculates its profit based on sales? It all starts with understanding relationships!
In this lesson, you'll learn how to take a linear equation, create a table of values from it, and then visually represent that relationship on a graph. This skill is fund...
2
Key Concepts & Vocabulary
TermDefinitionExample
Linear FunctionA function whose graph is a straight line. It describes a relationship where the rate of change is constant.The equation \( y = 2x + 1 \) is a linear function because its graph is a straight line.
Independent Variable (x)The input value of a function, which can be chosen freely. It is typically represented on the horizontal axis of a graph.In the function \( y = 3x - 5 \), 'x' is the independent variable. We choose values for 'x' to find 'y'.
Dependent Variable (y)The output value of a function, whose value depends on the independent variable. It is typically represented on the vertical axis of a graph.In the function \( y = 3x - 5 \), 'y' is the dependent variable. Its value changes based on the value of 'x...
3
Core Formulas
Standard Form of a Linear Equation (Slope-Intercept Form)
\( y = mx + b \)
This is a common way to write linear equations. 'm' represents the slope (rate of change), and 'b' represents the y-intercept (where the line crosses the y-axis). To complete a table, substitute chosen 'x' values into this equation to find 'y'.
Structure of an Ordered Pair
\( (x, y) \)
Every point on a coordinate plane is identified by an ordered pair. The first number, 'x', tells you how far to move horizontally (left or right from the origin). The second number, 'y', tells you how far to move vertically (up or down from the origin).
Plotting Points on a Coordinate Plane
Start at the origin \( (0,0) \). Move horizontally 'x'...
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
According to the tutorial, which of the following best defines a 'linear function'?
A.function whose graph is a curved line.
B.function whose graph is a straight line, indicating a constant rate of change.
C.Any equation that uses the variables 'x' and 'y'.
D.function that can only be represented by a table of values.
Easy
In the linear function equation y = mx + b, which variable is considered the 'independent variable'?
A.x
B.y
C.m
D.b
Easy
When plotting an ordered pair (x, y) from a table onto a coordinate plane, what does the 'y' value represent?
A.The horizontal movement from the origin.
B.The point where the line crosses the x-axis.
C.The slope of the line.
D.The vertical movement from the origin.
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