Solve Systems by Graphing

Front

What is a system of equations?

Back

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

Front

How do you solve a system of equations by graphing?

Back

To solve a system of equations by graphing, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect. This point is the solution to the system.

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

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

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 does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect, meaning they have no solution in the context of a system of equations.

Front

What does it mean for two lines to be perpendicular?

Back

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

Front

How can you determine the solution to a system of equations from a graph?

Back

The solution to a system of equations can be determined from a graph by finding the point where the two lines intersect. This point represents the values of x and y that satisfy both equations.

Front

What is the significance of the point (0, b) in the equation y = mx + b?

Back

The point (0, b) represents the y-intercept of the line, where the line crosses the y-axis.

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.