The graph of an equation represents the solution set of the equation, that is all the solutions of the equation are points that lie on the graph and all the points that lie on the graph are solutions of the equation.
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Normally no. But technically, it is possible if the two linear equations are identical.
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Not all equations have the coordinates 0,0 in their data range because not all equations pass through the origin when graphed
Related facts
They are different ways to represent the answers of an equation
Line graphs may represent equations, if they are defined for all values of a variable.
Bar graphs and line graphs do not. Straight line, parabolic, and hyperbolic graphs are graphs of an equation.
Graphs and equations of graphs that have at least one characteristic in common.
Equations are never parallel, but their graphs may be. -- Write both equations in "standard" form [ y = mx + b ] -- The graphs of the two equations are parallel if 'm' is the same number in both of them.
truetrue
They are straight line graphs that work out the solutions of 2 equations or simultaneous equations
graphs allow for an alternative visual method to solve mathematical equations.
Graphs are particularly useful in solving equations when you want to visualize the behavior of functions and their intersections. They can help identify solutions graphically, especially for nonlinear equations where algebraic methods may be complex. Additionally, using graphs allows for a quick assessment of the number of solutions and their approximate values. Overall, graphs are a valuable tool for understanding the relationships between variables in equations.
Tables, graphs, and equations are essential tools for working with proportions as they provide clear and organized ways to visualize relationships between quantities. Tables allow for easy comparison of values, making it straightforward to identify proportional relationships. Graphs illustrate these relationships visually, helping to identify trends and patterns. Equations enable precise calculations and manipulations, facilitating the solving of proportion-related problems.
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The graphs of systems of linear equations represent the relationships between variables, with each line corresponding to an equation. The point(s) where the lines intersect indicate the solution(s) to the system, showing where the equations are satisfied simultaneously. For systems of linear inequalities, the graphs display shaded regions that represent all possible solutions that satisfy the inequalities; the intersection of these regions highlights the feasible solutions. Therefore, both the graphs and their intersections are crucial for understanding the solutions to the systems.