MAYmester Check In: Analyze and Solve 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. This often involves adding, subtracting, multiplying, or dividing.

Front

What is the solution to the equation 4x + 1 = 7x - 5?

Back

The solution is x = 2.

Front

What steps are involved in solving the equation 2x + 5 = 12?

Back

1. Subtract 5 from both sides: 2x = 7. 2. Divide both sides by 2: x = 3.5.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same line when graphed.

Front

How can 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.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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

How do you solve the equation 6(2x + 1) = 18?

Back

1. Distribute: 12x + 6 = 18. 2. Subtract 6 from both sides: 12x = 12. 3. Divide by 12: x = 1.

Front

What is the y-intercept of the equation 20x - 18 = 12?

Back

To find the y-intercept, set x = 0. The equation becomes -18 = 12, which does not yield a valid y-intercept. However, the equation can be rearranged to find the intercepts.