Capture both of the lines by entering ordered pairs for points on these lines: y=2x+7 y=3x-3
To find points on each line, we can assign values to x and calculate the corresponding y values. Let's find the points on the first line, y = 2x + 7:
For x = 0:
y = 2(0) + 7
y = 0 + 7
y = 7
So the first point on the line y = 2x + 7 is (0, 7).
For x = 1:
y = 2(1) + 7
y = 2 + 7
y = 9
So the second point on the line y = 2x + 7 is (1, 9).
Now let's find points on the second line, y = 3x - 3:
For x = 0:
y = 3(0) - 3
y = 0 - 3
y = -3
So the first point on the line y = 3x - 3 is (0, -3).
For x = 1:
y = 3(1) - 3
y = 3 - 3
y = 0
So the second point on the line y = 3x - 3 is (1, 0).
Therefore, the ordered pairs representing points on these lines are:
Line 1: (0, 7), (1, 9)
Line 2: (0, -3), (1, 0)
To capture points on the line y = 2x + 7, we can choose any value for x and substitute it into the equation to find the corresponding y-value. Let's use x = 0, 1, and 2:
For x = 0:
y = 2(0) + 7
y = 0 + 7
y = 7
So the first point on the line y = 2x + 7 is (0, 7).
For x = 1:
y = 2(1) + 7
y = 2 + 7
y = 9
The second point on the line y = 2x + 7 is (1, 9).
For x = 2:
y = 2(2) + 7
y = 4 + 7
y = 11
The third point on the line y = 2x + 7 is (2, 11).
Now let's find points on the line y = 3x - 3:
For x = 0:
y = 3(0) - 3
y = 0 - 3
y = -3
The first point on the line y = 3x - 3 is (0, -3).
For x = 1:
y = 3(1) - 3
y = 3 - 3
y = 0
The second point on the line y = 3x - 3 is (1, 0).
For x = 2:
y = 3(2) - 3
y = 6 - 3
y = 3
The third point on the line y = 3x - 3 is (2, 3).
In summary, the ordered pairs for points on the line y = 2x + 7 are (0, 7), (1, 9), and (2, 11). The ordered pairs for points on the line y = 3x - 3 are (0, -3), (1, 0), and (2, 3).
To capture the points on the lines y = 2x + 7 and y = 3x - 3, you can choose any values for x and then substitute them into the equations to find the corresponding values of y.
Let's start with the line y = 2x + 7:
1. Choose a number for x. For example, let's take x = 0.
2. Substitute x = 0 into the equation y = 2x + 7:
y = 2(0) + 7
y = 0 + 7
y = 7
So, one point on the line y = 2x + 7 is (0, 7).
3. Repeat steps 1 and 2 with different values of x to get more points on the line. For instance, if we choose x = -2:
y = 2(-2) + 7
y = -4 + 7
y = 3
Thus, another point on the line y = 2x + 7 is (-2, 3).
You can continue this process to find more points on this line.
Now, let's move to the line y = 3x - 3:
1. Choose a value for x. For example, let's take x = 1.
2. Substitute x = 1 into the equation y = 3x - 3:
y = 3(1) - 3
y = 3 - 3
y = 0
Thus, one point on the line y = 3x - 3 is (1, 0).
3. Repeat steps 1 and 2 with different values of x to get more points on the line. For instance, if we choose x = -1:
y = 3(-1) - 3
y = -3 - 3
y = -6
Hence, another point on the line y = 3x - 3 is (-1, -6).
By following these steps, you can find more points on each line by choosing different values for x and substituting them into the corresponding equations.