5. Find three solutions of the equation y=9x-4.
(A) (-5, -49), (-2, -22), (3, 23)***
(B) (-5, -49), (2, -22), (3, 23)
(C) (-5, -49), (-2, -22), (-3, 23)
(D) (5, -49), (-2, 22), (-3, 23)
14. Which table shows a proportional relationship?
(A) x 1 3 4 6
y 2 4 6 7
(B) x 1 2 5 8
y -2 0 6 12
(C) x 2 3 5 6 ***
y -4 -6 -10 -12
(D) x 2 4 6 8
y 2 3 4 5
correct, and correct
I agree
To find three solutions of the equation y = 9x - 4, you need to substitute different values of x into the equation and solve for y. Let's check the options to see which set of values satisfies the equation.
(A) (-5, -49), (-2, -22), (3, 23)
For each pair, substitute the x-value into the equation:
For (-5, -49): y = 9(-5) - 4 = -45 - 4 = -49 (satisfies the equation)
For (-2, -22): y = 9(-2) - 4 = -18 - 4 = -22 (satisfies the equation)
For (3, 23): y = 9(3) - 4 = 27 - 4 = 23 (satisfies the equation)
So option (A) (-5, -49), (-2, -22), (3, 23) is correct.
To determine which table shows a proportional relationship, you need to check if the ratio of y to x remains constant across all values.
(A) x 1 3 4 6
y 2 4 6 7
To calculate the ratio: 2/1 = 4/3 = 6/4 = 7/6, which is not constant. So option (A) is not correct.
(B) x 1 2 5 8
y -2 0 6 12
To calculate the ratio: -2/1 = 0/2 = 6/5 = 12/8, which is not constant. So option (B) is not correct.
(C) x 2 3 5 6
y -4 -6 -10 -12
To calculate the ratio: -4/2 = -6/3 = -10/5 = -12/6, which is constant (-2). So option (C) is correct.
(D) x 2 4 6 8
y 2 3 4 5
To calculate the ratio: 2/2 = 3/4 = 4/6 = 5/8, which is not constant. So option (D) is not correct.
Therefore, option (C) x 2 3 5 6, y -4 -6 -10 -12 represents the proportional relationship.