Solving Linear Equations for y in Terms of x

The video tutorial explains how to work with equations involving two variables, focusing on standard and slope-intercept forms. It details the process of solving for Y in terms of X, emphasizing the use of the opposite property to manipulate equations. The tutorial includes examples to illustrate these concepts, demonstrating how to isolate Y and find ordered pairs on a graph. The video also touches on function notation and the importance of understanding these forms for graphing and solving equations.

What is the standard form of an equation with two variables?

• y = ax^2 + bx + c

• x^2 + y^2 = r^2

• ax + by = c

• y = mx + b

Why do we solve for y in terms of x?

• To make the equation more complex

• To find ordered pairs easily

• To eliminate the x variable

• To convert it to standard form

What is the first step in solving for y in terms of x?

• Subtract the constant term

• Divide by the coefficient of y

• Add the opposite of the x term

• Multiply by the reciprocal

When solving for y, why do we add the opposite of the x term?

• To make the equation simpler

• To convert it to standard form

• To eliminate the x term from one side

• To balance the equation

What do you do after adding the opposite of the x term when solving for y?

• Subtract the y term

• Add the constant term

• Divide by the coefficient of y

• Multiply by the reciprocal

In the example problem, what is the result of dividing each term by 3?

• y = 3x + 4

• y = 2x - 4

• y = 3x - 4

• y = 2x + 4

What is the final step in solving for y in terms of x?

• Multiply by the reciprocal

• Divide by the coefficient of y

• Add the constant term

• Subtract the x term

In the example problem, what do you do if y is negative?

• Multiply by -1

• Divide by the coefficient of y

• Leave it as is

• Add the opposite of y

What is the result of multiplying -1 by y and the other side of the equation?

• y = x - 17

• y = -x - 17

• y = -x + 17

• y = x + 17

Why is it important to make y positive when solving for y?

• To make the equation more complex

• To make the variable easier to interpret

• To simplify the equation

• To ensure the variable is in standard form