Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

How do you isolate a variable in a linear equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean if a linear equation has infinitely many solutions?

Back

It means that the equation represents the same line in a graph, and any point on that line is a solution.

Front

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

Back

It means that the equation represents two parallel lines that never intersect, indicating there are no points that satisfy both equations.

Front

What is the first step in solving the equation 4x - 40 = 7(-2x + 2)?

Back

The first step is to distribute the 7 on the right side of the equation.

Front

What is the solution to the equation 6x + 7 = 13 + 7x?

Back

The solution is x = -6.

Front

How do you check if your solution to a linear equation is correct?

Back

You substitute the solution back into the original equation to see if both sides are equal.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes; a positive slope means the line rises, while a negative slope means it falls.

Front

What is the y-intercept in the context of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.