Graphing and Solving Linear Equations

Front

What is a linear equation?

Back

Front

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 the x-value is substituted into the equation, the resulting y-value is equal to the y-value of the point.

Front

What is the slope-intercept form of a linear equation?

Back

Front

How do you find the slope of a line given two points?

Back

Front

What is the y-intercept of a linear equation?

Back

Front

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

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Front

How can you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation in the system. If all equations are satisfied, the point is a solution.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane, where each point on the line represents a solution to the equation.

Front

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.