The equation 3x + 2y = 4 represents a linear equation in two variables. To describe the graph of this equation, we can find its intercepts and understand its slope.
First, let’s find the x-intercept by setting y to 0:
- 3x + 2(0) = 4
- 3x = 4
- x = 4/3
This gives us the point (4/3, 0) for the x-intercept.
Now, let’s find the y-intercept by setting x to 0:
- 3(0) + 2y = 4
- 2y = 4
- y = 2
This gives us the point (0, 2) for the y-intercept.
Since the equation is in the form Ax + By = C, we can also find the slope. We can rearrange the equation to slope-intercept form (y = mx + b):
- 2y = -3x + 4
- y = -3/2x + 2
The slope (m) is -3/2, indicating that the line descends from left to right. Therefore, the graph is a straight line that crosses the y-axis at 2 and the x-axis at 4/3. Overall, the graph of 3x + 2y = 4 is a line that slopes downwards, indicating an inverse relationship between x and y values.