To find the slope and y-intercept of the equation given, we first need to rewrite it in the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Starting with the equation:
3y – 6x + 12 = 0
Let’s solve for y:
- First, isolate the term that contains y:
- Next, divide all terms by 3 to solve for y:
3y = 6x – 12
y = 2x – 4
Now, we can identify the slope and the y-intercept:
- The slope (m) is 2.
- The y-intercept (b) is -4.
Therefore, the slope of the line is 2, and the y-intercept is (0, -4). This means the line crosses the y-axis at -4 and for every unit increase in x, y increases by 2 units.