Mathematics
Grade 8
15 min
Graph a two-variable equation
Graph a two-variable equation
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1
Introduction & Learning Objectives
Learning Objectives
Identify the components of a two-variable linear equation.
Determine if an ordered pair is a solution to a two-variable equation.
Create a table of values for a given two-variable linear equation.
Accurately plot ordered pairs on a coordinate plane.
Graph a two-variable linear equation using a table of values.
Graph a two-variable linear equation using its slope-intercept form.
Ever wonder how maps help us find locations, or how a single line can represent countless possibilities? 🗺️ Get ready to unlock the power of visualizing equations!
In this lesson, you'll learn how to take an equation with two variables and turn it into a picture on a graph. This skill is crucial for understanding relationships between quantities and solving real-world problem...
2
Key Concepts & Vocabulary
TermDefinitionExample
Two-Variable EquationAn equation that contains two different variables, usually 'x' and 'y', representing two unknown quantities. When graphed, these equations often show a relationship between the two variables.y = 3x + 2 or 2x + 5y = 10
Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis). It's used to locate points using ordered pairs.The grid system where you plot points like (2, 3).
Ordered PairA pair of numbers (x, y) that represents a single point on the coordinate plane. The first number (x) indicates the horizontal position, and the second number (y) indicates the vertical position.(4, -1) means 4 units right from the origin and 1 unit down.
Soluti...
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Core Formulas
Rule for Graphing using a Table of Values
1. Choose at least three x-values (including positive, negative, and zero).
2. Substitute each x-value into the equation to find its corresponding y-value.
3. Form ordered pairs (x, y).
4. Plot these ordered pairs on the coordinate plane.
5. Draw a straight line connecting the points and extend it with arrows on both ends.
This method is fundamental for understanding how points satisfy an equation and form its graph. It works for any two-variable equation, but is particularly useful for linear equations.
Slope-Intercept Form of a Linear Equation
$$y = mx + b$$
This form directly gives you the slope (m) and the y-intercept (b) of a linear equation. 'm' represents the 'rise over run' (change in y divided by chan...
4 more steps in this tutorial
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Challenging
The points (1, 5) and (3, 9) are two solutions to a linear equation. What is the slope (m) of the line that represents this equation?
A.2
B.1/2
C.4
D.-2
Challenging
If the equation of a line is y = 2x + 1, what happens to the graph of the line if the equation is changed to y = 2x + 4?
A.The line becomes steeper.
B.The entire line shifts 3 units up.
C.The entire line shifts 3 units to the right.
D.The line becomes less steep.
Challenging
Which equation represents a line that has the same slope as y = 3x + 5 and the same y-intercept as y = -2x - 4?
A.y = 5x - 2
B.y = -2x + 5
C.y = 3x - 4
D.y = 3x + 5
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