1A 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 is the point(s) where the equations intersect on a graph.

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, 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 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.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.

Front

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

Back

To find the solution graphically, plot both equations on the same graph and identify the point where they 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.