2A 4.2 Practice: Systems from a Graph

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution to the system is the point(s) where the graphs of the equations intersect.

Front

What does the slope of a line represent in a linear equation?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

How do you determine the y-intercept from a linear equation in slope-intercept form?

Back

In the slope-intercept form of a linear equation, y = mx + b, the y-intercept is the value of b, which is the point where the line crosses the y-axis.

Front

What is the significance of the point of intersection in a system of linear equations?

Back

The point of intersection represents the solution to the system of equations, indicating the values of the variables that satisfy all equations in the system.

Front

How can you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, use the slope to find another point, and draw a straight line through the points.

Front

What is the difference between consistent and inconsistent systems of equations?

Back

A consistent system has at least one solution (intersecting lines), while an inconsistent system has no solutions (parallel lines that never intersect).

Front

What does it mean for a system of equations to be dependent?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Front

How do you find the solution to a system of equations graphically?

Back

To find the solution graphically, plot each equation on the same graph and identify the point(s) where the lines intersect.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

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

Back

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