Graphing Systems of Equations

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never intersect. They have the same slope.

Front

What does 'b' represent in the linear equation y = mx + b?

Back

'b' represents the y-intercept, the point where the line crosses the y-axis.

Front

What does it mean if two lines intersect at one point?

Back

It means the system of equations has one unique solution.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

How do you determine if two lines are parallel?

Back

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

Front

What is the solution to a system of equations?

Back

The solution is the point where the two lines intersect, representing the values of x and y that satisfy both equations.

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 is the y-intercept of the equation y = 4x + 5?

Back

The y-intercept is 5, which is the value of y when x = 0.

Front

How can you graph a linear equation?

Back

To graph a linear equation, find the y-intercept, plot it, then use the slope to find another point.

Front

What is the difference between intersecting lines and coincident lines?

Back

Intersecting lines have one solution (one point of intersection), while coincident lines have infinitely many solutions (they are the same line).