Understanding Solutions to Linear Equations

The video tutorial explains how to determine if ordered pairs are solutions to a given linear equation, both algebraically and graphically. It starts by defining the conditions for a solution and demonstrates the process of substitution to verify solutions algebraically. The tutorial then shows how to graph the equation and check if the points lie on the line, confirming the solutions. The video concludes by summarizing the results and reinforcing the methods used.

What must an ordered pair do to be considered a solution to a linear equation?

• It must have both negative values.

• It must be a point on the x-axis.

• It must have both positive values.

• It must make the equation true when substituted.

How can you determine if an ordered pair is a solution using a graph?

• By checking if the point lies on the line of the equation.

• By checking if the point lies on the y-axis.

• By checking if the point is at the origin.

• By checking if the point lies on the x-axis.

What is the algebraic method used for in this context?

• To find the slope of the line.

• To determine if an ordered pair is a solution.

• To calculate the y-intercept.

• To find the x-intercept.

What is the result of substituting the first ordered pair, (-2, -2.5), into the equation?

• The left side equals 11.

• The left side equals 9.

• The left side equals 7.

• The left side equals 5.

Why is the ordered pair (0, 4.5) not a solution to the equation?

• Because it results in a negative value.

• Because it results in a value greater than 7.

• Because it results in a value less than 7.

• Because it results in a value equal to 7.

What is the outcome when substituting the ordered pair (3, 12.5) into the equation?

• The left side equals 5.

• The left side equals 7.

• The left side equals 9.

• The left side equals 11.

What does the graphical representation show about the ordered pair (-2, -2.5)?

• It is below the line.

• It is above the line.

• It is on the line.

• It is not on the line.

Which ordered pair is not a solution according to the graph?

• (-2, -2.5)

• (3, 12.5)

• (0, 4.5)

• (1, 1)

What is the significance of the blue line in the graph?

• It represents the origin.

• It represents the equation.

• It represents the y-axis.

• It represents the x-axis.

What conclusion can be drawn from the graphical analysis?

• No ordered pairs are solutions.

• The graph does not provide any solutions.

• All ordered pairs are solutions.

• Only some ordered pairs are solutions.