Solutions on a graph

Front

What is a solution to a system of linear equations?

Back

A solution is a point (x, y) where the graphs of the equations intersect, meaning it satisfies all equations in the system.

Front

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

Back

Look for the point where the two lines intersect; this point gives the estimated solution (x, y).

Front

What does the point (4, 2) represent in the context of a graph of linear equations?

Back

It represents the coordinates where the two lines intersect, indicating the solution to the system of equations.

Front

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

Back

They represent the position of a point on the Cartesian plane, where 'x' is the horizontal distance from the origin and 'y' is the vertical distance.

Front

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

Back

It means they have no solutions in common, as they never intersect.

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 can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if it satisfies all equations, it is a solution.

Front

What is the y-intercept of a line?

Back

It is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does the slope of a line indicate?

Back

The slope indicates the steepness of the line and the direction it moves; a positive slope rises, while a negative slope falls.

Front

What is the purpose of graphing a system of equations?

Back

To visually find the solution(s) by identifying the intersection points of the lines.