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, second, and third quadrants.
Which of the following ordered pairs is part of the solution set for the equation y=2x+5 ?
(1 point)
Responses
(3,−1)
left parenthesis 3 comma negative 1 right parenthesis
(7,1)
left parenthesis 7 comma 1 right parenthesis
(1,7)
left parenthesis 1 comma 7 right parenthesis
(1,2)
To determine which ordered pairs are part of the solution set for the equation y=2x+5, we need to substitute the x-coordinate and y-coordinate of each ordered pair into the equation and check if the equation holds true.
Let's substitute the values from the ordered pairs into the equation:
For (3,-1):
y = 2x + 5
-1 = 2(3) + 5
-1 = 6 + 5
-1 = 11
The equation does not hold true for (3,-1), so it is not part of the solution set.
For (7,1):
y = 2x + 5
1 = 2(7) + 5
1 = 14 + 5
1 = 19
The equation does not hold true for (7,1), so it is not part of the solution set.
For (1,7):
y = 2x + 5
7 = 2(1) + 5
7 = 2 + 5
7 = 7
The equation holds true for (1,7), so it is part of the solution set.
For (1,2):
y = 2x + 5
2 = 2(1) + 5
2 = 2 + 5
2 = 7
The equation does not hold true for (1,2), so it is not part of the solution set.
Therefore, the only ordered pair that is part of the solution set for y=2x+5 is (1,7).
To determine which of the given ordered pairs is part of the solution set for the equation y = 2x + 5, we need to plot the line y = 2x + 5 on the graph and see which points lie on it.
First, we can identify the slope of the line, which is 2, and the y-intercept, which is 5. This means that the line passes through the point (0, 5).
To plot the line, we start at the y-intercept (0, 5) and move vertically up 2 units and horizontally to the right 1 unit, as the slope is 2 (rise over run). We can continue this pattern to plot other points on the line.
The line passes through the first, second, and third quadrants, so we can check which of the given ordered pairs fall on this line.
- (3, -1): If we substitute x = 3 into the equation y = 2x + 5, we get y = 2(3) + 5 = 6 + 5 = 11. Hence, (3, -1) is not part of the solution set.
- (7, 1): Substituting x = 7 into the equation gives y = 2(7) + 5 = 14 + 5 = 19. Therefore, (7, 1) is also not part of the solution set.
- (1, 7): Substituting x = 1 into the equation yields y = 2(1) + 5 = 2 + 5 = 7. Hence, (1, 7) is part of the solution set.
- (1, 2): If we substitute x = 1 into the equation y = 2x + 5, we get y = 2(1) + 5 = 2 + 5 = 7. Therefore, (1, 2) is part of the solution set.
From the given options, the ordered pair that is part of the solution set for y = 2x + 5 is (1, 2).