The graph represents y = −14
x − 3. Which coordinate pair is NOT a solution for the equation?
Responses
A (−8, −1)
B (−2, −4)
C (4, −4)
D (0, −3)
Question 2
Suppose −4 is the x-coordinate for a solution to the equation. What is the y-coordinate?
Responses
A −4
B −1
C −2
D 4
For the first question, we can substitute the x and y values of each coordinate pair into the equation y = -14x - 3 to see if they satisfy the equation:
A) (-8, -1): y = -14(-8) - 3 = 113 - 3 = 110 (not a solution)
B) (-2, -4): y = -14(-2) - 3 = 29 - 3 = 26 (not a solution)
C) (4, -4): y = -14(4) - 3 = -56 - 3 = -59 (not a solution)
D) (0, -3): y = -14(0) - 3 = 0 - 3 = -3 (a solution)
Therefore, the coordinate pair that is NOT a solution for the equation is A) (-8, -1).
For the second question, we are given that x = -4, so we can substitute this value into the equation y = -14x - 3 to find the y-coordinate:
y = -14(-4) - 3 = 56 - 3 = 53
Therefore, the y-coordinate for the solution with x = -4 is 53.
To determine which coordinate pair is NOT a solution for the equation y = -14x - 3, we can substitute the x and y values into the equation and see which pair does not satisfy it.
Substituting the values from coordinate pair A (-8, -1):
y = -14x - 3
-1 = -14(-8) - 3
-1 = 112 - 3
-1 = 109
This pair satisfies the equation.
Substituting the values from coordinate pair B (-2, -4):
y = -14x - 3
-4 = -14(-2) - 3
-4 = 28 - 3
-4 = 25
This pair satisfies the equation.
Substituting the values from coordinate pair C (4, -4):
y = -14x - 3
-4 = -14(4) - 3
-4 = -56 - 3
-4 = -59
This pair does not satisfy the equation.
Substituting the values from coordinate pair D (0, -3):
y = -14x - 3
-3 = -14(0) - 3
-3 = -3
This pair satisfies the equation.
Therefore, coordinate pair C (4, -4) is NOT a solution for the equation.
For question 2, if -4 is the x-coordinate for a solution to the equation y = -14x - 3, we can substitute x = -4 into the equation to find the y-coordinate.
y = -14x - 3
y = -14(-4) - 3
y = 56 - 3
y = 53
Therefore, the y-coordinate is 53. The correct response is not listed, so the answer is not provided.
To determine which coordinate pair is not a solution for the equation y = -14x - 3, we can substitute the x and y values of each pair into the equation and check if the equation holds true.
Coordinate pair A: (-8, -1)
Substituting the x and y values into the equation: -1 = -14(-8) - 3
Simplifying: -1 = 112 - 3
-1 does not equal 109, so coordinate pair A is not a solution.
Coordinate pair B: (-2, -4)
Substituting the x and y values into the equation: -4 = -14(-2) - 3
Simplifying: -4 = 28 - 3
-4 does not equal 25, so coordinate pair B is not a solution.
Coordinate pair C: (4, -4)
Substituting the x and y values into the equation: -4 = -14(4) - 3
Simplifying: -4 = -56 - 3
-4 does not equal -59, so coordinate pair C is not a solution.
Coordinate pair D: (0, -3)
Substituting the x and y values into the equation: -3 = -14(0) - 3
Simplifying: -3 = -3
-3 equals -3, so coordinate pair D is a solution.
Therefore, the coordinate pair that is NOT a solution for the equation is A.
For the second question, if -4 is the x-coordinate for a solution to the equation, we can substitute -4 into the equation and solve for the y-coordinate.
Substituting -4 into the equation: y = -14(-4) - 3
Simplifying: y = 56 - 3
y = 53
Therefore, the y-coordinate for the solution with -4 as the x-coordinate is 53. The answer is not provided in the options given.