Complete the table for the equation 3x−4y=12, and graph the equation.
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Part 1
x
y
0
negative 3−3
Part 2
44
0
Part 3
−4
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Here is the completed table for the equation 3x - 4y = 12:
Part 1:
x y
0 -3
3 0
Part 2:
x y
4 0
12 9
Part 3:
x y
-4 -6
To graph the equation 3x - 4y = 12, plot the points from the table on a coordinate plane and connect them with a straight line.
To complete the table for the equation 3x - 4y = 12, we need to substitute the given values of x and solve for y.
Part 1:
When x = 0, we have:
3(0) - 4y = 12
0 - 4y = 12
-4y = 12
y = -3
Part 2:
When y = 0, we have:
3x - 4(0) = 12
3x - 0 = 12
3x = 12
x = 4
Part 3:
When x = -4, we have:
3(-4) - 4y = 12
-12 - 4y = 12
-4y = 12 + 12
-4y = 24
y = -6
Now, let's graph the equation on a coordinate plane:
- Start by plotting the points we found in the table: (0, -3), (4, 0), and (-4, -6).
- Use a ruler to draw a straight line passing through these points.
- Note that the line extends infinitely in both directions.
The graph of the equation 3x - 4y = 12 is a straight line passing through the points (0, -3), (4, 0), and (-4, -6).
To complete the table for the equation 3x - 4y = 12, we need to substitute different values of x and calculate the corresponding values of y.
Part 1:
Given x = 0, we can substitute this into the equation:
3(0) - 4y = 12
0 - 4y = 12
Solving this equation, we find:
-4y = 12
Dividing both sides by -4:
y = -3
So, when x = 0, y = -3.
Part 2:
Given y = 0, we can substitute this into the equation:
3x - 4(0) = 12
3x - 0 = 12
3x = 12
Dividing both sides by 3:
x = 4
So, when y = 0, x = 4.
Part 3:
Given x = -4, we can substitute this into the equation:
3(-4) - 4y = 12
-12 - 4y = 12
-4y = 12 + 12
-4y = 24
Dividing both sides by -4:
y = -6
So, when x = -4, y = -6.
Now, let's graph the equation on a coordinate plane:
To graph the equation 3x - 4y = 12, we can use the slope-intercept form, which is y = mx + b.
Let's rearrange the given equation to solve for y:
3x - 4y = 12
-4y = -3x + 12
Divide both sides by -4:
y = (3/4)x - 3
From this equation, we can see that the slope is 3/4 and the y-intercept is -3.
To graph the equation:
1. Plot the y-intercept, which is the point (0, -3).
2. Use the slope of 3/4 to find other points on the line. For example, starting from the y-intercept, move up 3 units and right 4 units, and plot another point. Repeat this process to find more points.
3. Connect the points with a straight line.
The graph of the equation 3x - 4y = 12 would look like this:
(Graph) The graph will be a straight line passing through the points (0,-3), (4,0), (-4,-6), and more points you might have calculated.