Linear Equations and Their Graphs

The video tutorial explains how to identify linear and nonlinear equations based on the exponents of variables. It demonstrates graphing linear equations by plotting points and connecting them to form a straight line. The tutorial also covers strategies for dealing with fractions in equations, emphasizing the importance of choosing appropriate values to simplify calculations. Throughout, the video highlights the consistent nature of linear equations and their graphical representation as straight lines.

What distinguishes a linear equation from a nonlinear equation?

• The type of operations used

• The presence of variables

• The exponents of the variables

• The number of variables

In the equation x + y = 6, which of the following points is a solution?

• (3, 2)

• (2, 3)

• (1, 5)

• (0, 5)

What pattern do the points of the equation x + y = 6 form on a graph?

• A curve

• A circle

• A zigzag line

• A straight line

How many points are needed at minimum to graph a linear equation?

• Four

• Three

• Two

• One

What is the y-value when x = 0 in the equation 3x + y = -8?

• 8

• -8

• 0

• 3

If you choose x = 3 for the equation 1/3x - y = 2, what is the value of y?

• 2

• -1

• 1

• -2

What is the result of substituting x = -6 in the equation 1/3x - y = 2?

• y = 4

• y = -4

• y = 2

• y = -2

Which x-value would simplify calculations in the equation 1/3x - y = 2?

• 4

• 5

• 3

• 2

In the equation 4x - 3y = 12, what is the x-value when y = 0?

• 4

• 3

• 12

• 0

What is the y-value when x = 0 in the equation 4x - 3y = 12?

• 12

• 4

• 0

• -4