Solving and Graphing Linear Equations

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 represented by the value of b in the equation y = mx + b.

Front

How do you solve a linear equation with one variable?

Back

To solve a linear equation with one variable, isolate the variable on one side of the equation using inverse operations.

Front

What does it mean if a linear equation has no solution?

Back

If a linear equation has no solution, it means that the lines represented by the equations are parallel and will never intersect.

Front

What is the graphical representation of the equation y = -x + 2?

Back

The graph of y = -x + 2 is a straight line with a slope of -1 and a y-intercept of 2.

Front

How do you determine if two linear equations are equivalent?

Back

Two linear equations are equivalent if they have the same slope and y-intercept, meaning they represent the same line.

Front

What is the process for graphing a linear equation?

Back

To graph a linear equation, find 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 does it mean to solve for a variable?

Back

To solve for a variable means to find the value of that variable that makes the equation true.

Front

What is the significance of the solution to a system of linear equations?

Back

The solution to a system of linear equations represents the point(s) where the lines intersect, indicating the values of the variables that satisfy all equations in the system.