Linear equations (two variables)

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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What does it mean for a point to be a solution to a linear equation?

Back

A point (x, y) is a solution to a linear equation if, when you substitute x and y into the equation, the equation is true.

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What is the slope in a linear equation?

Back

The slope (m) is a number that describes how steep the line is. It represents the change in y for a one-unit change in x.

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What is the y-intercept in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It is the value of y when x is 0.

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How do you check if a point is a solution to an equation?

Back

To check if a point (x, y) is a solution, substitute x and y into the equation. If both sides of the equation are equal, then it is a solution.

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What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point on a graph, written as (x, y).

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What does it mean if a point satisfies an equation?

Back

If a point satisfies an equation, it means that when you plug the point's coordinates into the equation, the equation holds true.

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions to the system are points that satisfy all equations in the system.

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What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution if there are no points that satisfy all equations at the same time.

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What does it mean for a system of equations to have infinitely many solutions?

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.