Complete the table for the equation 3x−4y=12, and graph the equation.
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Part 1
x
y
0
enter your response here
Part 1:
x y
0 -3
4 0
8 3
To graph the equation 3x-4y=12, we can rewrite it in slope-intercept form, y = (3/4)x - 3.
The graph would be a straight line passing through the points (0,-3), (4,0), and (8,3).
To complete the table for the equation 3x - 4y = 12, we substitute the given values of x into the equation and solve for y.
For x = 0:
3(0) - 4y = 12
0 - 4y = 12
-4y = 12
y = -3
Thus, the completed table is as follows:
x | y
0 | -3
Now, let's graph the equation 3x - 4y = 12:
To graph the equation, we can rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Start by isolating y:
3x - 4y = 12
-4y = -3x + 12
y = (3/4)x - 3
Now we have the equation in slope-intercept form, with a slope of 3/4 and a y-intercept of -3.
To graph the line, plot the y-intercept at (0, -3) and use the slope to find additional points. The slope of 3/4 means that for every increase of 4 in the x-direction, we have an increase of 3 in the y-direction. So, starting from the y-intercept, move 4 units to the right and 3 units up to find another point. Connect the two points with a straight line.
The graph of the equation 3x - 4y = 12 would look like a straight line passing through the points (0, -3) and (4, 0).
To complete the table for the equation 3x-4y=12, we need to find the corresponding values of x and y that satisfy the equation.
We can start by choosing a value for x and then solve for y.
For the first row, let's start with x = 0.
Plug in x = 0 into the equation and solve for y:
3(0) - 4y = 12
0 - 4y = 12
-4y = 12
Divide both sides by -4:
y = -12/4
y = -3
So, for x = 0, we have y = -3.
Now you can continue completing the table by selecting different values for x and solving for y using the same process.