Graphing Linear Systems

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.

Front

What does it mean to graph a system of equations?

Back

Graphing a system of equations involves plotting the equations on the same coordinate plane to find their point of intersection, which represents the solution.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

What does it mean if two lines are parallel when graphing?

Back

If two lines are parallel, it means they have the same slope and will never intersect, indicating that the system has no solution.

Front

What does it mean if two lines coincide when graphing?

Back

If two lines coincide, they lie on top of each other and have infinitely many solutions, as every point on the line is a solution.

Front

How do you find the slope of a line from an equation?

Back

The slope of a line can be found from the equation in slope-intercept form (y = mx + b) where m represents the slope.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How can you determine if a system of equations has one solution?

Back

A system of equations has one solution if the lines intersect at exactly one point, meaning they have different slopes.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

The graph of y = 2x + 1 is a straight line with a slope of 2 and a y-intercept at (0, 1).

Front

How do you solve a system of equations by graphing?

Back

To solve by graphing, plot each equation on the same coordinate plane and identify the point where they intersect.