The graph represents y = −14
x − 3. Which coordinate pair is NOT a solution for the equation?
Responses
A (−8, −1)(−8, −1)
B (−2, −4)(−2, −4)
C (4, −4)(4, −4)
D (0, −3)(0, −3)
Question 2
Suppose −4 is the x-coordinate for a solution to the equation. What is the y-coordinate?
Responses
A −4−4
B −1−1
C −2−2
D 4
For the first question, we can substitute the x and y coordinates of each answer choice into the equation y = -14x - 3 to see if they satisfy the equation.
A: (-8, -1)
-1 = -14(-8) - 3
-1 = 112 - 3
-1 = 109, which is not true. Therefore, (A) is not a solution.
B: (-2, -4)
-4 = -14(-2) - 3
-4 = 28 - 3
-4 = 25, which is not true. Therefore, (B) is not a solution.
C: (4, -4)
-4 = -14(4) - 3
-4 = -56 - 3
-4 = -59, which is not true. Therefore, (C) is not a solution.
D: (0, -3)
-3 = -14(0) - 3
-3 = -3, which is true. Therefore, (D) is a solution.
Therefore, the coordinate pair that is NOT a solution for the equation y = -14x - 3 is choice (A) (-8, -1).
For the second question, we are given that -4 is the x-coordinate.
We can substitute -4 into the equation y = -14x - 3 to find the y-coordinate.
y = -14(-4) - 3
y = 56 - 3
y = 53
Therefore, the y-coordinate is 53. The correct answer choice is (D) 53.
To determine which coordinate pair is NOT a solution for the equation y = -14x - 3, we can substitute the x and y values from each coordinate pair into the equation and check if the equation holds true.
A) (−8, −1):
Substituting x = -8 and y = -1, we get:
-1 = -14(-8) - 3
-1 = 112 - 3
-1 = 109
Since -1 is not equal to 109, this coordinate pair is NOT a solution.
B) (−2, −4):
Substituting x = -2 and y = -4, we get:
-4 = -14(-2) - 3
-4 = 28 - 3
-4 = 25
Since -4 is not equal to 25, this coordinate pair is NOT a solution.
C) (4, −4):
Substituting x = 4 and y = -4, we get:
-4 = -14(4) - 3
-4 = -56 - 3
-4 = -59
Since -4 is not equal to -59, this coordinate pair is NOT a solution.
D) (0, −3):
Substituting x = 0 and y = -3, we get:
-3 = -14(0) - 3
-3 = 0 - 3
-3 = -3
Since -3 is equal to -3, this coordinate pair is a solution.
Therefore, the coordinate pair NOT a solution for the equation y = -14x - 3 is (A) (−8, −1).
For the second question, if x = -4 is a solution to the equation y = -14x - 3, we can substitute x = -4 into the equation to find the y-coordinate.
Substituting x = -4, we get:
y = -14(-4) - 3
y = 56 - 3
y = 53
So, if x = -4 is a solution to the equation, the y-coordinate 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 of each pair into the equation and check if it holds true.
Let's go through each option:
A) (-8, -1):
Substituting x = -8, y = -1 into the equation, we get -1 = -14(-8) - 3 = 111.
So (-8, -1) is not a solution for the equation.
B) (-2, -4):
Substituting x = -2, y = -4 into the equation, we get -4 = -14(-2) - 3 = -25.
So (-2, -4) is a solution for the equation.
C) (4, -4):
Substituting x = 4, y = -4 into the equation, we get -4 = -14(4) - 3 = -59.
So (4, -4) is not a solution for the equation.
D) (0, -3):
Substituting x = 0, y = -3 into the equation, we get -3 = -14(0) - 3 = -3.
So (0, -3) is a solution for the equation.
Therefore, the coordinate pair that is not a solution for the equation is (C) (4, -4).
For the second question, we're given that x = -4 is a solution to the equation. To find the corresponding y-coordinate, we can substitute x = -4 into the equation and solve for y.
Substituting x = -4 into the equation y = -14x - 3, we get:
y = -14(-4) - 3
y = 56 - 3
y = 53
So, if x = -4 is a solution, then the corresponding y-coordinate is 53.
Therefore, the answer to the second question is (D) 53.