The graph of -6x + 12y = 24 is a straight line with a positive slope of 1/2 and a y-intercept of 2. The line extends infinitely in both directions.
To understand the graph of the linear equation -6x + 12y = 24, it's helpful to express it in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Starting with the given equation:
-6x + 12y = 24
Add 6x to both sides:
12y = 6x + 24
Divide both sides by 12:
![\[ y = (1)/(2)x + 2 \]](https://img.qammunity.org/2024/formulas/mathematics/college/9rn8pvuyqwp4v3bdzqgxclqrle4vl5jefv.png)
Now, the equation is in slope-intercept form, where the slope (m) is 1/2 and the y-intercept (b) is 2.
This means the graph is a line with a slope of 1/2 (rise over run) and passes through the point (0, 2) on the y-axis.
In summary, the graph of -6x + 12y = 24 is a straight line with a positive slope of 1/2 and a y-intercept of 2. The line extends infinitely in both directions.
The probable question may be:
Explain the graph of the linear equation -6x +12y = 24