Graph as a Picture of Solutions
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to understand the graph of an equation as a visual representation of all its solutions. Every point on the graph satisfies the equation, making the graph a complete picture of all (x, y) pairs that make the equation true.
Key Concepts
Property The graph of an equation is a picture of the solutions of the equation. Each point on the graph represents a solution. If a point lies on the graph, its coordinates make the equation true. When you graph a linear equation, you should extend the line far enough in both directions so that it will cross both the $x$ axis and the $y$ axis.
Examples For the equation $y = 3x 1$, the point $(2, 5)$ is a solution because when we substitute $x=2$, we get $y = 3(2) 1 = 5$. Therefore, the point $(2, 5)$ lies on the graph of the line.
To solve $3x 1 = 8$ using the graph of $y = 3x 1$, we find the point on the line where the y coordinate is 8. The corresponding x coordinate for that point is 3, so $x=3$ is the solution.
Common Questions
What does the graph of an equation represent?
The graph of an equation is the set of all (x, y) coordinate pairs that satisfy the equation. Every point on the line or curve is a solution.
How do you check if a point is on the graph of an equation?
Substitute the x and y values of the point into the equation. If the equation is true, the point is on the graph.
Why is the graph called a picture of solutions?
Because every point on the graph is a solution to the equation, the graph visually displays all solutions at once.
What are the coordinates of a solution on a graph?
Each solution is a coordinate pair (x, y) that makes the equation true. For a linear equation, all solutions lie on a straight line.
Where is the graph as a picture of solutions taught?
This concept is introduced in the Yoshiwara Elementary Algebra textbook for Grade 6 students.