Understanding Ordered Pairs and Absolute Value Equations

The video tutorial explains how to determine if specific ordered pairs satisfy the equation y = |x - 4| - 2. It involves substituting x and y values from each pair into the equation and simplifying to check for true statements. The tutorial evaluates several pairs, confirming which ones are solutions. Additionally, it demonstrates using a graph to verify solutions visually.

What is the first step in determining if an ordered pair satisfies the equation y = |x - 4| - 2?

• Graph the equation on a coordinate plane.

• Substitute the values of x and y into the equation.

• Check if the ordered pair is a solution to another equation.

• Calculate the slope of the line.

Why does the ordered pair (-3, 5) satisfy the equation y = |x - 4| - 2?

• Because the absolute value of -3 is negative.

• Because -3 is greater than 4.

• Because 5 is less than 2.

• Because 5 equals the absolute value of -3 minus 4 minus 2.

What is the result of substituting the ordered pair (3, 1) into the equation y = |x - 4| - 2?

• 1 equals 1, which is true.

• 1 equals -1, which is false.

• 3 equals -3, which is false.

• 3 equals 3, which is true.

How does the ordered pair (4, -2) satisfy the equation y = |x - 4| - 2?

• The absolute value of 4 minus 4 is 2.

• The absolute value of 4 minus 4 is -2.

• The absolute value of 4 minus 4 is 0.

• The absolute value of 4 minus 4 is 4.

What is the outcome when substituting the ordered pair (10, 3) into the equation y = |x - 4| - 2?

• 3 equals 6, which is true.

• 3 equals 3, which is true.

• 3 equals 2, which is false.

• 3 equals 4, which is false.

What is the result of substituting the ordered pair (0, 2) into the equation y = |x - 4| - 2?

• 2 equals 2, which is true.

• 2 equals 4, which is false.

• 2 equals 0, which is false.

• 2 equals -2, which is true.

How can you verify if an ordered pair is a solution to the equation y = |x - 4| - 2 graphically?

• By checking if the point lies on the origin.

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

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

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

Which ordered pairs were found to be solutions to the equation y = |x - 4| - 2?

• (-3, 5), (3, 1), (10, 3)

• (0, 2), (4, -2), (10, 3)

• (-3, 5), (0, 2), (4, -2)

• (3, 1), (4, -2), (10, 3)

Which ordered pairs were not solutions to the equation y = |x - 4| - 2?

• (-3, 5) and (0, 2)

• (4, -2) and (0, 2)

• (3, 1) and (10, 3)

• (-3, 5) and (10, 3)

What shape does the graph of the equation y = |x - 4| - 2 form?

• A circle

• A straight line

• A V-shape

• A parabola