2. Which ordered pair is a solution of y = x – 4? (1 point)
(−1, −5) (0, −3) (2, 6) (3, 1)
3. Which is a graph of the equation y = 2x − 4? (1 point)
4. Which equation has (2, −1) as a solution? (1 point)
y = 2x − 1 y= x+ 3 y= x– 3
y = −2x + 1
#2. Just check each (x,y) pair to see whether y = x-4
-5 = -1-4, so (-1,-5) is a solution
#3 any function of the form y = mx+b where m and b are just numbers, is a straight line
#4 Just like #2. Plug in x and y to see whether the equation is true.
2. To determine which ordered pair is a solution of y = x - 4, substitute the x-coordinate and y-coordinate of each ordered pair into the equation and see if the equation holds true.
For the ordered pair (-1, -5):
substituting -1 for x and -5 for y in the equation y = x - 4:
-5 = -1 - 4
-5 = -5
Since -5 is equal to -5, the equation holds true for the ordered pair (-1, -5).
For the ordered pair (0, -3):
substituting 0 for x and -3 for y in the equation y = x - 4:
-3 = 0 - 4
-3 = -4
Since -3 is not equal to -4, the equation does not hold true for the ordered pair (0, -3).
For the ordered pair (2, 6):
substituting 2 for x and 6 for y in the equation y = x - 4:
6 = 2 - 4
6 = -2
Since 6 is not equal to -2, the equation does not hold true for the ordered pair (2, 6).
For the ordered pair (3, 1):
substituting 3 for x and 1 for y in the equation y = x - 4:
1 = 3 - 4
1 = -1
Since 1 is not equal to -1, the equation does not hold true for the ordered pair (3, 1).
Therefore, the ordered pair (-1, -5) is the solution of y = x - 4.
3. To determine which graph represents the equation y = 2x - 4, we can look for the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
For the equation y = 2x - 4, the slope is 2 and the y-intercept is -4.
Looking at the answer choices, we can eliminate any graphs that do not have a slope of 2 or a y-intercept of -4.
The correct graph representing the equation y = 2x - 4 would be the one that has a slope of 2 and a y-intercept of -4.
4. To find which equation has (2, -1) as a solution, we can substitute the x-coordinate and y-coordinate of the point into each equation and see if the equation holds true.
For the equation y = 2x - 1:
substituting 2 for x and -1 for y in the equation:
-1 = 2(2) - 1
-1 = 4 - 1
-1 = 3
Since -1 is not equal to 3, the equation does not hold true for the point (2, -1).
For the equation y = x + 3:
substituting 2 for x and -1 for y in the equation:
-1 = 2 + 3
-1 = 5
Since -1 is not equal to 5, the equation does not hold true for the point (2, -1).
For the equation y = x - 3:
substituting 2 for x and -1 for y in the equation:
-1 = 2 - 3
-1 = -1
Since -1 is equal to -1, the equation holds true for the point (2, -1).
Therefore, the equation y = x - 3 has (2, -1) as a solution.
To find the solution to a given equation or determine which equation satisfies certain conditions, you need to substitute the values of the ordered pairs into the equation and see if they make the equation true. Let's go through each question one by one:
2. Which ordered pair is a solution of y = x – 4?
To find the solution, substitute the x and y values of each ordered pair into the equation y = x - 4 and check if the equation holds true.
Let's check the ordered pairs one by one:
- For the ordered pair (-1, -5), substitute x = -1 and y = -5 into the equation: -5 = -1 - 4. This equation is true, so (-1, -5) is a solution.
- For the ordered pair (0, -3), substitute x = 0 and y = -3 into the equation: -3 = 0 - 4. This equation is not true, so (0, -3) is not a solution.
- For the ordered pair (2, 6), substitute x = 2 and y = 6 into the equation: 6 = 2 - 4. This equation is not true, so (2, 6) is not a solution.
- For the ordered pair (3, 1), substitute x = 3 and y = 1 into the equation: 1 = 3 - 4. This equation is true, so (3, 1) is a solution.
Therefore, the correct answer is (−1, −5) as it is the ordered pair that satisfies the equation y = x – 4.
3. Which is a graph of the equation y = 2x − 4?
To visualize the graph of the equation y = 2x - 4, you can plot a few points using various x-values and then connect them to get a straight line. The equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.
By using different x-values and substituting them into the equation, you can find the corresponding y-values. Let's choose a few values:
For x = -2, y = 2(-2) - 4 = -4 - 4 = -8.
For x = 0, y = 2(0) - 4 = -4.
For x = 2, y = 2(2) - 4 = 4 - 4 = 0.
Using these points, you can plot them on a Cartesian plane and draw a line passing through them. The correct graph will show a straight line passing through the points (-2, -8), (0, -4), and (2, 0).
4. Which equation has (2, −1) as a solution?
To check which equation has (2, -1) as a solution, substitute the x and y values of the ordered pair into each equation and see if they make the equation true.
Let's check the equations one by one:
- For the equation y = 2x - 1: Substitute x = 2 and y = -1. The equation becomes -1 = 2(2) - 1. This equation is true, so y = 2x - 1 has (2, -1) as a solution.
- For the equation y = x + 3: Substitute x = 2 and y = -1. The equation becomes -1 = 2 + 3. This equation is not true, so y = x + 3 does not have (2, -1) as a solution.
- For the equation y = x - 3: Substitute x = 2 and y = -1. The equation becomes -1 = 2 - 3. This equation is not true, so y = x - 3 does not have (2, -1) as a solution.
- For the equation y = -2x + 1: Substitute x = 2 and y = -1. The equation becomes -1 = -2(2) + 1. This equation is true, so y = -2x + 1 has (2, -1) as a solution.
Therefore, the correct equation that has (2, -1) as a solution is y = 2x - 1.