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
negative 6−6
Part 4
enter your response here
3
To find the corresponding values of y for each given value of x, we can rearrange the equation 3x - 4y = 12 to solve for y:
3x - 4y = 12
-4y = -3x + 12
y = (-3x + 12) / -4
y = (3/4)x - 3
Now we can plug in the given values of x to find the corresponding values of y:
Part 1:
x = 0
y = (3/4)(0) - 3
y = -3
So, the table entry for Part 1 is: (0, -3)
Part 2:
x = 44
y = (3/4)(44) - 3
y = 33 - 3
y = 30
So, the table entry for Part 2 is: (44, 30)
Part 3:
x = -4
y = (3/4)(-4) - 3
y = -3 - 3
y = -6
So, the table entry for Part 3 is: (-4, -6)
Part 4:
x = 3
y = (3/4)(3) - 3
y = 9/4 - 3
y = 9/4 - 12/4
y = -3/4
So, the table entry for Part 4 is: (3, -3/4)
Now we can plot these points on a graph and draw the line connecting them to represent the given equation. The x-axis and y-axis should be labeled appropriately.
To complete the table for the equation 3x - 4y = 12, we need to substitute the given x-values into the equation and solve for the corresponding y-values.
Part 1:
When x = 0,
3(0) - 4y = 12
-4y = 12
Divide both sides by -4:
y = -3
So, when x = 0, y = -3.
Part 2:
When x = 4,
3(4) - 4y = 12
12 - 4y = 12
Subtract 12 from both sides:
-4y = 0
Divide both sides by -4:
y = 0
So, when x = 4, y = 0.
Part 3:
When x = -4,
3(-4) - 4y = 12
-12 - 4y = 12
Subtract -12 from both sides:
-4y = 24
Divide both sides by -4:
y = -6
So, when x = -4, y = -6.
Part 4:
When x = 3,
3(3) - 4y = 12
9 - 4y = 12
Subtract 9 from both sides:
-4y = 3
Divide both sides by -4:
y = -3/4
So, when x = 3, y = -3/4.
Now let's graph the equation 3x - 4y = 12 on a coordinate plane. To do this, we'll plot the points from the completed table and draw a straight line passing through them.
The graph should have these points:
(0, -3)
(4, 0)
(-4, -6)
(3, -3/4)
Now, plot these points on a coordinate plane. Once all points are plotted, draw a straight line passing through them.
To complete the table for the equation 3x - 4y = 12, we can substitute the given values of x into the equation to solve for y.
Part 1:
When x = 0,
3(0) - 4y = 12
0 - 4y = 12
-4y = 12
Dividing both sides by -4, we get:
y = -3
So, when x = 0, y = -3.
Part 2:
When y = 0,
3x - 4(0) = 12
3x - 0 = 12
3x = 12
Dividing both sides by 3, we get:
x = 4
So, when y = 0, x = 4.
Part 3:
When x = -4,
3(-4) - 4y = 12
-12 - 4y = 12
-4y = 12 + 12
-4y = 24
Dividing both sides by -4, we get:
y = -6
So, when x = -4, y = -6.
Part 4:
When x = 3,
3(3) - 4y = 12
9 - 4y = 12
-4y = 12 - 9
-4y = 3
Dividing both sides by -4, we get:
y = -3/4
So, when x = 3, y = -3/4.
Now, let's graph the equation 3x - 4y = 12:
To graph the equation, we can start by finding two points on the line using the values we found in the table.
Plot the points (0, -3) and (4, 0) on a coordinate plane. Then, draw a straight line passing through these two points.
The graph of the equation 3x - 4y = 12 will be a straight line passing through the points (0, -3) and (4, 0).