Complete the table for the equation 3x−2y=6, and graph the equation.
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Part 1
x
y
0
negative 3−3
Part 2
22
0
Part 3
−2
enter your response here
For Part 1:
To find the value of y when x = 0, we can substitute x = 0 into the equation and solve for y:
3(0) - 2y = 6
-2y = 6
y = -3
Therefore, when x = 0, y = -3.
For Part 2:
To find the value of y when x = 2, we can substitute x = 2 into the equation and solve for y:
3(2) - 2y = 6
6 - 2y = 6
-2y = 0
y = 0
Therefore, when x = 2, y = 0.
For Part 3:
To find the value of y when x = -2, we can substitute x = -2 into the equation and solve for y:
3(-2) - 2y = 6
-6 - 2y = 6
-2y = 12
y = -6
Therefore, when x = -2, y = -6.
The completed table is as follows:
x | y
------------------
0 | -3
2 | 0
-2 | -6
Now we can graph the equation 3x - 2y = 6:
Plot the points (0, -3), (2, 0), and (-2, -6) on the coordinate plane and draw a straight line passing through these points.
The graph of the equation is a straight line that passes through the points (0, -3), (2, 0), and (-2, -6).
To complete the table for the equation 3x - 2y = 6, we can substitute the given values of x into the equation and solve for y. Here is the completed table:
Part 1:
x y
0 -3
1 1.5
2 3
3 4.5
4 6
Part 2:
x y
2 0
5 6
8 12
Part 3:
x y
-2 -5
-5 -9
-8 -13
To graph the equation 3x - 2y = 6, you can plot the points from the completed table on the coordinate plane and connect them with a straight line.
To complete the table for the equation 3x - 2y = 6, we need to substitute different values of x and solve for y.
For Part 1, when x = 0, we have:
3(0) - 2y = 6
0 - 2y = 6
-2y = 6
y = 6/(-2)
y = -3
So, for Part 1, the values for x and y are:
x = 0
y = -3
For Part 2, when x = 2, we have:
3(2) - 2y = 6
6 - 2y = 6
-2y = 6 - 6
-2y = 0
y = 0/(-2)
y = 0
So, for Part 2, the values for x and y are:
x = 2
y = 0
For Part 3, when x = -2, we have:
3(-2) - 2y = 6
-6 - 2y = 6
-2y = 6 + 6
-2y = 12
y = 12/(-2)
y = -6
So, for Part 3, the values for x and y are:
x = -2
y = -6
Now, let's graph the equation. To graph the equation 3x - 2y = 6, we need to convert it to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Starting with the original equation:
3x - 2y = 6
First, we isolate y:
-2y = -3x + 6
y = (3/2)x - 3
Now we have the equation in slope-intercept form. The slope (m) is 3/2 and the y-intercept (b) is -3.
To graph the equation, we can start by plotting the y-intercept. In this case, the y-intercept is -3, so we plot the point (0, -3).
Next, we use the slope to find additional points on the graph. The slope of 3/2 means that for every increase of 2 in x, y increases by 3. We can use this information to plot additional points. For example, if we start at (0, -3), we can move 2 units to the right and 3 units up to get another point: (2, 0).
Repeat this process to find more points, if desired.
Once you have several points, you can connect them with a straight line to graph the equation.
I hope this explanation helps you complete the table and graph the equation. Let me know if you have any further questions!