Given the ordered pairs of points:
(-5, 20), (0, -5), (1, -4), (4, 11)
Let's dtetermine the equation that can be used to generate the given set of ordered pairs.
Input the value of x and y in the equation, if the equation turns out to be true, i.e the left side equals the right side for all ordered pairs, then the equation can be used to generate the set of ordered pairs.
Let's start from the first equation.
• Equation A.
y = -6x - 10
(-5, 20)
Substitute -5 for x and 20 for y:
20 = -6(-5) - 10
20 = 30 - 10
20 = 20
(0, -5):
Substitute 0 for x and -5 for y:
-5 = -6(0) - 10
-5 = 0 - 10
-5 ≠ -10
Since this equation is not true for the second ordered pair, this equation A cannot be used to generate the given set of ordered pairs.
• Equation B.
y = x² - 5
(-5, 20):
Substitute -5 for x and 20 for y
20 = -5² - 5
20 = 25 - 5
20 = 20
(0, -5):
Substitute 0 for x and -5 for y
-5 = 0² - 5
-5 = 0 -5
-5 = -5
(1, -4):
Substitue 1 for x nd -4 for y
-4 = 1² - 5
-4 = 1 - 5
-4 = -4
(4, 11)
Substitute 4 for x and 11 for y
11 = 4² - 5
11 = 16 - 5
11 = 11
Here, the equation is true for all set of ordered pairs. Therefore, we can say this equation (y = x² - 5) can be used to generate the given set of ordered pairs.
ANSWER:
B. y = x² - 5