What is the equation of the line that goes through the point (2, 2) and is parallel to the line represented by the equation y = rac{1}{2}x + 8?

To find the equation of the line that passes through the point (2, 2) and is parallel to the given line y = rac{1}{2}x + 8, we need to follow these steps:

1. Identify the slope: The given line has a slope (m) of rac{1}{2}, as indicated by the coefficient of x in the slope-intercept form (y = mx + b). Since parallel lines have the same slope, our new line will also have a slope of rac{1}{2}.
2. Use the point-slope form: Next, we can use the point-slope formula to find our new line’s equation. The point-slope form is given by:

y - y_1 = m(x - x_1)

In our case, (x₁, y₁) is the point (2, 2) and m is rac{1}{2}. Plugging in these values:

y - 2 = rac{1}{2}(x - 2)

3. Simplify the equation: Now we simplify the equation:

y - 2 = rac{1}{2}x - 1

Next, add 2 to both sides to solve for y:

y = rac{1}{2}x + 1

So, the equation of the line that passes through the point (2, 2) and is parallel to the line y = rac{1}{2}x + 8 is:

y = rac{1}{2}x + 1

This is our final answer!