Graph the following linear equation using one of the following methods:

1st slope intercept form y = mx + b
2nd table of values
3rd x-intercept and y-intercept

1. 3x + 4y = 12

intercepts are easiest

when x=0, 4y=12, so y=3
when y=0, 3x=12, so, x=4

So, plot the points (0,3) and (4,0) and draw a line through them.

To graph the linear equation 3x + 4y = 12, we have multiple methods to choose from. Let's use the slope-intercept form y = mx + b.

1. Slope-intercept form (y = mx + b):
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line, and b represents the y-intercept (the point where the line crosses the y-axis).

First, solve the equation for y:
3x + 4y = 12
4y = -3x + 12
y = (-3/4)x + 3

Now we have the equation in slope-intercept form (y = mx + b) with m = -3/4 and b = 3.

Start by plotting the y-intercept (0, b), where b = 3. Mark the point (0, 3) on the graph.

Next, use the slope to find another point on the graph. The slope -3/4 means that for every increase of 4 units in the x-coordinate, the corresponding y-coordinate decreases by 3 units.

From the y-intercept (0, 3), move 4 units to the right (increase x by 4) and 3 units down (decrease y by 3). Mark this new point on the graph.

Now draw a straight line passing through both points. This line represents the graph of the linear equation 3x + 4y = 12.

2. Table of values:
To generate a table of values, you can select various x-values and substitute them into the equation to find the corresponding y-values.

Choose a few values for x, for example, -2, 0, and 2. Substitute these values one at a time into the equation 3x + 4y = 12 and solve for y:

For x = -2:
3(-2) + 4y = 12
-6 + 4y = 12
4y = 18
y = 4.5

So, we have the first point (-2, 4.5).

For x = 0:
3(0) + 4y = 12
4y = 12
y = 3

So, we have the second point (0, 3).

For x = 2:
3(2) + 4y = 12
6 + 4y = 12
4y = 6
y = 1.5

So, we have the third point (2, 1.5).

Plot these points (-2, 4.5), (0, 3), and (2, 1.5) on the graph and connect them using a straight line.

3. X-intercept and y-intercept:
To find the x-intercept, let y = 0, and solve for x:
3x + 4(0) = 12
3x = 12
x = 4

So, the x-intercept is (4, 0).

To find the y-intercept, let x = 0, and solve for y:
3(0) + 4y = 12
4y = 12
y = 3

So, the y-intercept is (0, 3).

Plot the x-intercept (4, 0) and the y-intercept (0, 3) on the graph, and draw a line passing through them. This line represents the graph of the linear equation 3x + 4y = 12.