What is the slope-intercept form of the line that is perpendicular to 3x - 2y = 8 and passes through the point (-1, -1)?

To determine the correct slope-intercept form of the line that is perpendicular to the given equation (3x - 2y = 8) and passes through the point ((-1, -1)), we first need to find the slope of the line described by the equation.

1. Convert to slope-intercept form (y = mx + b): Start with the equation (3x - 2y = 8). Rearranging it, we can isolate (y):

[

-2y = -3x + 8

]

[

y = \frac{3}{2}x - 4

]

From this form, we see that the slope (m) of the line is (\frac{3}{2}).

2. Find the slope of the perpendicular line: The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. Consequently, the negative reciprocal of (\frac{3}{2}) is (-\frac{2}{3}).

3. Use the point-slope form to find the equation of the new line: We have the slope (-