Final answer:
To find the equation of a line perpendicular to the given line and passing through the given point, we use the negative reciprocal of the slope of the given line and the point-slope form of the equation of a line.
Step-by-step explanation:
To find the equation of a line perpendicular to a given line and passing through a given point, we first need to determine the slope of the given line. The equation of the given line is y = 0.5x + 1. Comparing this equation with the standard form y = mx + b, we can see that the slope of the given line is 0.5. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. Therefore, the slope of the line perpendicular to the given line is -2.
Next, we can use the point-slope form of the equation of a line to write the equation. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values (-1, -1) for (x1, y1) and -2 form, the equation becomes y - (-1) = -2(x - (-1)). Simplifying further, we get y + 1 = -2(x + 1).