Graph of the Equation 3x - 4y + 6 = 0
Understanding the Equation:
- The equation 3x - 4y + 6 = 0 is a linear equation in two variables x and y.
- It represents a straight line on the Cartesian plane.
Graphing the Equation:
- To graph the equation, we can rewrite it in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
- Rearranging the equation, we get: y = (3/4)x + 3/2.
- The slope of the line is 3/4, meaning for every 3 units moved in the positive x-direction, we move 4 units in the positive y-direction.
- The y-intercept is at (0, 3/2), which is where the line crosses the y-axis.
- We can plot the y-intercept and then use the slope to find more points on the line.
- After plotting several points, we can connect them to draw a straight line representing the equation 3x - 4y + 6 = 0.
Analyzing the Graph:
- The graph of the equation 3x - 4y + 6 = 0 will be a straight line sloping upwards from left to right.
- The line will pass through the point (0, 3/2) on the y-axis.
- Any point lying on this line will satisfy the equation 3x - 4y + 6 = 0.
Conclusion:
- By graphing the equation 3x - 4y + 6 = 0, we can visually represent the relationship between x and y as defined by the equation.
- This graph provides a geometric representation of the solution set of the linear equation.