Graphing Systems of Linear Equations

Front

What is a solution to a system of linear equations?

Back

A solution is a set of (x,y) coordinates that satisfy both equations in the system.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope.

Front

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

Back

It means the lines are parallel and will never intersect.

Front

What does it mean if a system of equations has an infinite number of solutions?

Back

It means the lines are the same, overlapping each other.

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

Front

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

Back

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

Front

What is the y-intercept of the equation y = -2x + 5?

Back

The y-intercept is 5, which is the point (0, 5) on the graph.

Front

How do you find the intersection point of two lines graphically?

Back

The intersection point is where the two lines cross each other on the graph.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes (upward or downward).

Front

If two lines have different slopes, what can you conclude about their intersection?

Back

If two lines have different slopes, they will intersect at exactly one point.