Final answer:
To find the equation in slope-intercept form for the line that passes through the given point and is perpendicular to the given equation, we first determine the slope of the given equation. Then we use the point-slope form of a linear equation and plug in the values to find the equation in slope-intercept form.
Step-by-step explanation:
To find an equation in slope-intercept form that is perpendicular to the given equation and passes through the given point, we need to determine the slope of the given equation. The slope of the given equation y = -1/3x + 9 is -1/3 because it is in the form y = mx + b, where m is the slope.
The slope of a line perpendicular to this is the negative reciprocal of -1/3, which is 3. Now we can use the point-slope form of a linear equation, y - y1 = m(x - x1), with the point (-2,-2) and the slope 3 to find the equation. Plugging in the values, we get y - (-2) = 3(x - (-2)). Simplifying, we get y + 2 = 3(x + 2), which can be written in slope-intercept form as y = 3x + 4.