Solving 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 'solving a linear equation' mean?

Back

Solving a linear equation means finding the value of the variable that makes the equation true.

Front

What is the slope in a linear equation?

Back

The slope (m) is a number that describes the steepness and direction of a line. It is calculated as the rise over run.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform operations to get the variable on one side of the equation and all other terms on the other side.

Front

What is the first step in solving the equation 2x + 3 = 11?

Back

The first step is to subtract 3 from both sides of the equation to get 2x = 8.

Front

What do you do after isolating the variable in an equation?

Back

After isolating the variable, you perform the necessary operations to find its value.

Front

What is the solution to the equation 2x = 8?

Back

The solution is x = 4, found by dividing both sides by 2.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there is no value for the variable that makes the equation true, often resulting in a false statement.

Front

What is an example of a linear equation with no solution?

Back

An example is 2x + 3 = 2x + 5, which simplifies to 3 = 5, a false statement.