Graphing Systems of Linear Equations

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

The two lines are the same line.

Front

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

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine if two lines are parallel when graphing?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What does it mean if a system of equations has no solution?

Back

The graph of the equations represents parallel lines.

Front

What is the solution to the system of equations represented by the lines that intersect at a point?

Back

The solution is the coordinates of the intersection point.

Front

How can you solve a system of linear equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the point of intersection.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x.

Front

If two lines have different slopes, what can be said about their intersection?

Back

They will intersect at exactly one point.

Front

What is the graphical representation of a system with exactly one solution?

Back

The lines intersect at a single point.