Final answer:
To solve the equation y = -1/3x^9 for slope-intercept form, the slope is -1/3 and the y-intercept is 0. Therefore, the correct option is d) Slope = -1/3; y-intercept = 3.
Step-by-step explanation:
To solve for the equation of a line in slope-intercept form that is perpendicular to the given line y = -1/3x⁹ and passes through the point (-2, -2), we need to understand that the slope of the required line will be the negative reciprocal of the slope of the given line.
Since the slope of the given line is -1/3, the slope of a line perpendicular to it is 3. Once we have the slope, we can use the point-slope formula to derive the equation of the line.
To solve the equation y = -1/3x^9 for slope-intercept form, we need to rearrange the equation into the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation is already in slope-intercept form. The slope is -1/3, which means for every 1 unit increase in x, y will decrease by 1/3 unit.
The y-intercept is 0, since the equation does not contain a constant term. Therefore, the correct option is d) Slope = -1/3; y-intercept = 3.