How to Graph the Equation 4x + 3y = 12?

To graph the equation 4x + 3y = 12, we first need to rewrite it in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.

1. Start by isolating y:

3y = -4x + 12

2. Next, divide every term by 3:

y = -\frac{4}{3}x + 4

Now we can identify the slope (-4/3) and the y-intercept (4). This means that the line crosses the y-axis at (0, 4).

3. To graph the line, we need another point. We can find this by choosing a value for x and solving for y. Let’s choose x = 0:

y = -\frac{4}{3}(0) + 4 = 4

The point (0, 4) is one point on the line. Now, let’s find another point by choosing x = 3:

y = -\frac{4}{3}(3) + 4 = -4 + 4 = 0

Now, we have another point (3, 0). We can plot both points on a graph: (0, 4) and (3, 0).

4. Finally, draw a straight line through the points. The line should extend in both directions, indicating that it represents all the solutions to the equation 4x + 3y = 12.

This is how you graph the equation step-by-step!