Linear Equations and Systems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept in 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 = 0.

Front

How do you solve a system of linear equations?

Back

You can solve a system of linear equations using methods such as substitution, elimination, or graphing to find the point where the lines intersect.

Front

What is the solution to a system of linear equations?

Back

The solution to a system of linear equations is the point (x, y) that satisfies all equations in the system.

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.

Front

What does it mean for two lines to be perpendicular?

Back

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

Front

What is a direct proportion?

Back

A direct proportion is a relationship between two variables where their ratio is constant. If one variable increases, the other increases at a constant rate.

Front

How do you graph a linear equation?

Back

To graph a linear equation, you can find two or more points that satisfy the equation and then draw a straight line through those points.

Front

What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by adding or subtracting equations to eliminate one variable.