Final answer:
To convert the equation y - 2 = 3(x + 1) to slope-intercept form, distribute the slope and isolate y to get y = 3x + 5, which is the correct slope-intercept form.
Step-by-step explanation:
The equation provided, y - 2 = 3(x + 1), is initially in point-slope form. To convert it to slope-intercept form, we need to solve for y. Here's how it's done step-by-step:
- Distribute the slope (which is 3) across the (x + 1) on the right side of the equation, so it becomes 3x + 3.
- Add 2 to both sides of the equation to isolate y, resulting in y = 3x + 3 + 2.
- Combine like terms, which gives us y = 3x + 5, which is the slope-intercept form of the equation.
The term m represents the slope, and b represents the y-intercept in the slope-intercept form of a line (y = mx + b). In our example, the slope (m) is 3, and the y-intercept (b) is 5.