1. Determine which ordered pair is a solution of y = x^2-2
(5, 21),
(–5, 24),
(–1, –1), ••
(–2, 6)
2. Without graphing, tell whether the line containing (6, –3) and (0, –8) is horizontal, vertical, or neither
I think it's horizontal
Correct my answers
1 yes
horizontal means both y vaues the same. -3 is not -8
vertical means both x values the same. 6 is not 0
To determine if an ordered pair is a solution of a given equation, you need to substitute the values of the ordered pair into the equation and check if the equation is true.
For question 1, we're given the equation y = x^2 - 2. Let's evaluate each ordered pair:
1. (5, 21): Substitute x = 5 into the equation:
y = (5)^2 - 2
y = 25 - 2
y = 23
Since y ≠ 21, (5, 21) is not a solution.
2. (–5, 24): Substitute x = -5 into the equation:
y = (-5)^2 - 2
y = 25 - 2
y = 23
Since y ≠ 24, (–5, 24) is not a solution.
3. (–1, –1): Substitute x = -1 into the equation:
y = (-1)^2 - 2
y = 1 - 2
y = -1
Since y = -1, (–1, –1) is a solution.
4. (–2, 6): Substitute x = -2 into the equation:
y = (-2)^2 - 2
y = 4 - 2
y = 2
Since y ≠ 6, (–2, 6) is not a solution.
So, the ordered pair (–1, –1) is the solution of the equation y = x^2 - 2.
For question 2, to determine if the line is horizontal, vertical, or neither, we need to compare the y-coordinates of the two points.
Given points: (6, –3) and (0, –8)
If the y-coordinates are the same, the line is horizontal. If the x-coordinates are the same, the line is vertical. Otherwise, the line is neither horizontal nor vertical.
Comparing the y-coordinates of the two points, we have -3 and -8. Since they are different, the line is neither horizontal nor vertical.
So, your answer that the line containing (6, –3) and (0, –8) is neither horizontal nor vertical is correct.