Final answer:
The slope of the line represented by the equation -2x + 6y = 12 is 1/3. This is determined by rewriting the equation in slope-intercept form, y = mx + b, which highlights that the line rises 1 unit up for every 3 units it moves to the right.
Step-by-step explanation:
The question asks us to find the slope of the line represented by the equation -2x + 6y = 12. To find the slope, we need to rewrite the equation in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. We start by adding 2x to both sides of the equation and then divide everything by 6 to solve for y:
-2x + 6y = 12
6y = 2x + 12
y = (2x/6) + (12/6)
y = (1/3)x + 2
From this, we can see that the slope (m) of the line is 1/3. This means there is a rise of 1 unit on the vertical axis for every increase of 3 units on the horizontal axis. The slope is always constant along a straight line, indicating the consistent steepness of the line, and in this case, the line rises as we move to the right since the slope is positive.
The value of the slope can tell us a lot about the graph of a line. A positive slope indicates the line moves upward as the x-values increase. Conversely, a negative slope means the line moves downward. If the slope is zero, the line is horizontal, and if it is undefined (due to division by zero), the line is vertical. The steepness of the line is directly associated with the absolute value of the slope: the larger the number, the steeper the line.