The equation 3x + 2y = 4 is a linear equation in two variables, x and y. To understand what the graph of this equation represents, let’s break it down step by step.
The first step in exploring the graph is to rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To do this, we can isolate y:
2y = -3x + 4
y = - rac{3}{2}x + 2Now, from the rewritten equation, we can see that:
- The slope (m) is -3/2, which means for every 2 units you move to the right on the x-axis, you move 3 units down on the y-axis. This indicates that the line will slope downwards.
- The y-intercept (b) is 2. This means that the line crosses the y-axis at the point (0, 2).
Based on this information, the graph of 3x + 2y = 4 will be a straight line that descends from left to right, starting at the point (0, 2) on the y-axis. Additionally, you can find another point on the line by substituting a value for x. For example, if you let x = 0, then y = 2; if you let x = 2, then:
y = - rac{3}{2}(2) + 2
y = -3 + 2 = -1This gives you the additional point (2, -1). Plotting these points and drawing a line through them will give you the graph of the equation.
In conclusion, the graph of the equation 3x + 2y = 4 represents a straight line that slopes downward, with a y-intercept at (0, 2) and passing through other points such as (2, -1).