Which of the following is an ordered pair of the relation y equals 2/3x + 6?
There are no options provided in the question. Could you please provide the options so I can identify which one is an ordered pair of the relation y equals 2/3x + 6?
A. ( zero, -2/3)
b. ( three, eight)
c. (three, four)
d. (one, four)
To determine which of the given options is an ordered pair of the relation y = 2/3x + 6, we need to substitute the given x-values into the equation and see if the resulting y-value matches the corresponding y-value in each ordered pair.
y = 2/3x + 6
a. Substituting x = 0:
y = 2/3(0) + 6
y = 0 + 6
y = 6
The ordered pair (0, 6) does not match with option A: (0, -2/3)
b. Substituting x = 3:
y = 2/3(3) + 6
y = 2 + 6
y = 8
The ordered pair (3, 8) matches with option B: (3, 8)
c. Substituting x = 3:
y = 2/3(3) + 6
y = 2 + 6
y = 8
The ordered pair (3, 8) does not match with option C: (3, 4)
d. Substituting x = 1:
y = 2/3(1) + 6
y = 2/3 + 6
y = 8/3 + 6 = 26/3
y ≈ 8.67
The ordered pair (1, 8.67) does not match with option D: (1, 4)
Therefore, the ordered pair (three, eight) fits the relation y = 2/3x + 6, which corresponds to option B.
Which of the following gives an example of a function that is not linear?
a. 9x + 3y - 18 = 0
b. Y equals 1/6 x + 2/3
c. 2x + 3y = 16
d. y equals x to the power of 2 minus 3x plus 2.25
A function that is not linear has a graph that is not a straight line. Let's analyze each given option to determine which provides an example of a function that is not linear:
a. 9x + 3y - 18 = 0
Rearranging the equation into slope-intercept form (y = mx + b), we get:
3y = -9x + 18
y = -3x + 6
This equation is linear since it represents a straight-line graph.
b. y = 1/6x + 2/3
This equation is linear since it represents a straight-line graph.
c. 2x + 3y = 16
Rearranging the equation into slope-intercept form:
3y = -2x + 16
y = -2/3x + 16/3
This equation is linear since it represents a straight-line graph.
d. y = x^2 - 3x + 2.25
This equation is not linear because of the x^2 term. It represents a quadratic function with a graph that is a parabola, not a straight line.
Therefore, the option that provides an example of a function that is not linear is:
d. y = x^2 - 3x + 2.25