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Graphs of Linear Equations 3
Question 1
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
Question 1: The coordinate pair that is NOT a solution for the equation y = -14x - 3 is D) (0, -3).
Question 2: If -4 is the x-coordinate for a solution to the equation, the y-coordinate would be A) -4.
Question 1: The graph represents y = -14x - 3. We need to determine which coordinate pair is NOT a solution for the equation.
To find the answer, we can evaluate each given coordinate pair by substituting the x and y values into the equation and checking if the equation holds.
A: (-8, -1)
Substituting x = -8 and y = -1 into the equation:
-1 = -14*(-8) - 3
-1 = 112 - 3
-1 = 109 (not true)
B: (-2, -4)
Substituting x = -2 and y = -4 into the equation:
-4 = -14*(-2) - 3
-4 = 28 - 3
-4 = 25 (not true)
C: (4, -4)
Substituting x = 4 and y = -4 into the equation:
-4 = -14*(4) - 3
-4 = -56 - 3
-4 = -59 (not true)
D: (0, -3)
Substituting x = 0 and y = -3 into the equation:
-3 = -14*(0) - 3
-3 = 0 - 3
-3 = -3 (true)
Therefore, the coordinate pair that is NOT a solution for the equation is option A: (-8, -1).
Question 2: Suppose -4 is the x-coordinate for a solution to the equation. We need to find the corresponding y-coordinate.
To find the solution, we can substitute x = -4 into the equation and solve for y.
Substituting x = -4 into the equation y = -14x - 3:
y = -14*(-4) - 3
y = 56 - 3
y = 53
Therefore, the y-coordinate for the x-coordinate -4 is 53.
The answers are:
Question 1: Option A (-8, -1) is NOT a solution for the equation.
Question 2: The y-coordinate for the x-coordinate -4 is 53.
To solve question 1, we need to determine which coordinate pair is not a solution for the equation y = -14x - 3. To do this, we can substitute each coordinate pair into the equation and check if it satisfies the equation. The correct answer is the coordinate pair that does not satisfy the equation.
Let's substitute each coordinate pair into the equation:
A. (-8, -1): Substitute x = -8 and y = -1 into the equation:
-1 = -14*(-8) - 3
Simplifying:
-1 = 112 - 3
-1 = 109
Since -1 is not equal to 109, coordinate pair A is not a solution.
B. (-2, -4): Substitute x = -2 and y = -4 into the equation:
-4 = -14*(-2) - 3
Simplifying:
-4 = 28 - 3
-4 = 25
Since -4 is not equal to 25, coordinate pair B is not a solution.
C. (4, -4): Substitute x = 4 and y = -4 into the equation:
-4 = -14*4 - 3
Simplifying:
-4 = -56 - 3
-4 = -59
Since -4 is not equal to -59, coordinate pair C is not a solution.
D. (0, -3): Substitute x = 0 and y = -3 into the equation:
-3 = -14*0 - 3
Simplifying:
-3 = 0 - 3
-3 = -3
Since -3 is equal to -3, coordinate pair D is a solution.
Therefore, the coordinate pair that is NOT a solution for the equation y = -14x - 3 is A. (-8, -1).
To solve question 2, we are given that -4 is the x-coordinate for a solution to the equation. We need to find the corresponding y-coordinate. To do this, we can substitute x = -4 into the equation y = -14x - 3 and solve for y.
Let's substitute x = -4 into the equation:
y = -14*(-4) - 3
Simplifying:
y = 56 - 3
y = 53
Therefore, when x = -4, the y-coordinate is 53. The answer to question 2 is option D. 53.