Solutions on a graph

Front

What is a solution to a system of linear equations?

Back

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

Front

How can you estimate the solution of a system of linear equations from a graph?

Back

By identifying the point where the two lines intersect on the graph.

Front

What does it mean if two lines on a graph are parallel?

Back

It means there is no solution to the system of equations, as the lines will never intersect.

Front

What does it mean if two lines on a graph coincide?

Back

It means there are infinitely many solutions, as every point on the line is a solution to the system.

Front

What is the significance of the coordinates (x, y) in a solution?

Back

They represent the values of the variables that satisfy the equations in the system.

Front

If the solution to a system of equations is (3, 0), what does this indicate?

Back

It indicates that when x = 3 and y = 0, both equations in the system are satisfied.

Front

What is the graphical representation of the equation y = mx + b?

Back

It is a straight line where m is the slope and b is the y-intercept.

Front

How do you find the y-intercept of a linear equation from a graph?

Back

The y-intercept is the point where the line crosses the y-axis (where x = 0).

Front

What is the slope of a line?

Back

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

Front

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

Back

It means the lines representing the equations are parallel and do not intersect.