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 ax + b = c, where a, b, and c are constants.

Front

What does it mean to solve a linear equation?

Back

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

Front

What is the solution of the equation 2x + 3 = 7?

Back

The solution is x = 2.

Front

What is the first step in solving the equation x + 5 = 12?

Back

The first step is to subtract 5 from both sides of the equation.

Front

What is the purpose of isolating the variable in an equation?

Back

Isolating the variable helps to find its value by getting it alone on one side of the equation.

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.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of how steep the line is, calculated as the rise over run.

Front

What does the y-intercept represent in a linear equation?

Back

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

Front

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

Back

You can check your solution by substituting the value back into the original equation to see if both sides are equal.