Final answer:
To find the equation of a line that goes through the point (-2, 9) and is parallel to the line y = 1/2x - 1, we use the point-slope form with the same slope, 1/2, resulting in y = 1/2x + 10.
Step-by-step explanation:
The equation of the line that goes through the point (-2, 9) and is parallel to the line y = \(\frac{1}{2}\)x - 1 can be found using the concept of slope. The given line has a slope of \(\frac{1}{2}\), and because parallel lines have the same slope, the slope of our new line will also be \(\frac{1}{2}\). A line's equation is generally given by y = mx + b, where m is the slope and b is the y-intercept. Since we want our line to pass through (-2, 9) and have a slope of \(\frac{1}{2}\), we can use the point-slope form which is y - y_1 = m(x - x_1), where \((x_1, y_1)\) is the point given. Substituting the given points and slope into this formula, we get:
y - 9 = \(\frac{1}{2}\)(x + 2)
Expanding and simplifying this, we get the final equation:
y = \(\frac{1}{2}\)x + 10