To convert the linear equation 2x + 3y = 6 into slope-intercept form, we need to solve for y.
- Start with the original equation: 2x + 3y = 6.
- Subtract 2x from both sides to isolate the term with y: 3y = 6 – 2x.
- Next, divide every term by 3 to solve for y: y = 2 – rac{2}{3}x.
Now, we can rearrange the equation to highlight the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
From our equation, we can see that:
- The slope (m) is - rac{2}{3}.
- The y-intercept (b) is 2, which means the line crosses the y-axis at (0, 2).
Thus, the slope-intercept form of the linear equation 2x + 3y = 6 is y = - rac{2}{3}x + 2.