Final answer:
To find the equation of the perpendicular line, we determine the slope of the given line is -2, meaning our new line has a slope of 1/2. Using the point (-2, 2) and the slope 1/2 in the point-slope form, we determine the perpendicular line's equation.
Step-by-step explanation:
To write the equation of a line that passes through the point (-2, 2) and is perpendicular to the line given by 6x + 3y = -9, we first need to determine the slope of the given line. By rearranging the equation into slope-intercept form, we find that the slope (m) of the given line is -2, because the equation transforms into y = -2x - 3. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of our new line will be 1/2.
To find the equation of our new line, we use the point-slope form which is (y - y1) = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope. Substituting the values, we get (y - 2) = ¹⁄₂(x + 2). By rearranging it to slope-intercept form, we find the equation of the line that passes through (-2, 2) and is perpendicular to 6x + 3y = -9.