Use the image to answer the question.
A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of 5. A line passes through the first, third, and fourth quadrants.
Which of the following ordered pairs is part of the solution set for the equation y=3x−4
?
Option #1: (−1,0)
Option #2: (0,−4)
Option #3: (3,4)
(1 point)
Option #
is part of the solution set for the
The ordered pairs represent points on the graph. We can determine if a point is part of the solution set by substituting the x and y-values into the equation and seeing if both sides are equal.
Let's check each option:
Option #1: (−1,0)
Substituting x = -1 and y = 0 into the equation:
0 = 3(-1) - 4
0 = -3 - 4
0 = -7
Since -7 is not equal to 0, option #1 is not part of the solution set.
Option #2: (0,−4)
Substituting x = 0 and y = -4 into the equation:
-4 = 3(0) - 4
-4 = -4
Since -4 is equal to -4, option #2 is part of the solution set.
Option #3: (3,4)
Substituting x = 3 and y = 4 into the equation:
4 = 3(3) - 4
4 = 9 - 4
4 = 5
Since 4 is not equal to 5, option #3 is not part of the solution set.
Therefore, the correct answer is option #2: (0, -4).
To determine if a given point is part of the solution set for the equation y = 3x - 4, we need to substitute the values of the x and y coordinates of the point into the equation and see if it holds true.
Let's start with each option one by one:
Option #1: (-1, 0)
To check if this point is part of the solution set, substitute x = -1 and y = 0 into the equation:
0 = 3(-1) - 4
0 = -3 - 4
0 = -7
Since the equation does not hold true for this option, (-1, 0) is not part of the solution set.
Option #2: (0, -4)
To check if this point is part of the solution set, substitute x = 0 and y = -4 into the equation:
-4 = 3(0) - 4
-4 = -4
Since the equation holds true for this option, (0, -4) is part of the solution set.
Option #3: (3, 4)
To check if this point is part of the solution set, substitute x = 3 and y = 4 into the equation:
4 = 3(3) - 4
4 = 9 - 4
4 = 5
Since the equation does not hold true for this option, (3, 4) is not part of the solution set.
Therefore, the only ordered pair that is part of the solution set for the equation y = 3x - 4 is Option #2: (0, -4).