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A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of 5. A line passes through the first, third, and fourth quadrants.

Which of the following ordered pairs is part of the solution set for the equation y=2.5x−2

?

Option #1: (−2,0)

Option #2: (2,5)

Option #3: (2,3)

(1 point)
Option #
is part of the solution set for the equation.

1 answer

To determine which ordered pair is part of the solution set for the equation \( y = 2.5x - 2 \), we need to substitute the x-value from each option into the equation and see if the resulting y-value matches the y-value given in the ordered pair.

  1. Option #1: \( (-2, 0) \) \[ y = 2.5(-2) - 2 = -5 - 2 = -7 \] The ordered pair is \( (-2, 0) \), but the calculated y-value is \(-7\). So this option is not a solution.

  2. Option #2: \( (2, 5) \) \[ y = 2.5(2) - 2 = 5 - 2 = 3 \] The ordered pair is \( (2, 5) \), but the calculated y-value is \(3\). So this option is not a solution.

  3. Option #3: \( (2, 3) \) \[ y = 2.5(2) - 2 = 5 - 2 = 3 \] The ordered pair is \( (2, 3) \), and the calculated y-value is \(3\). This matches, so this option is a solution.

So the answer is Option #3: \( (2, 3) \) is part of the solution set for the equation \( y = 2.5x - 2 \).