To find the equation of the line that passes through the point (2, 2) and is parallel to the line given by the equation y = (1/2)x + 8, we first need to determine the slope of the original line. The equation is in slope-intercept form, y = mx + b, where m represents the slope.
In this case, the slope m of the line y = (1/2)x + 8 is 1/2. Since parallel lines have the same slope, the line we want to find will also have a slope of 1/2.
Next, we can use the point-slope form of a linear equation, which is given by:
y – y1 = m(x – x1)
where (x1, y1) is the point the line passes through (in this case, (2, 2)), and m is the slope. Plugging in the values:
y – 2 = (1/2)(x – 2)
Now, we can simplify this equation:
y – 2 = (1/2)x – 1
Adding 2 to both sides gives us:
y = (1/2)x + 1
Thus, the equation of the line that passes through the point (2, 2) and is parallel to y = (1/2)x + 8 is:
y = (1/2)x + 1