Final answer:
The equation of the line perpendicular to -8x + 9y = 82 and passing through the point (-8, -2) in slope-intercept form is y = -9/8x - 11/4.
Step-by-step explanation:
The line perpendicular to -8x + 9y = 82 will have a slope that is the negative reciprocal of the slope of the given line. First, we need to rearrange the equation into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. Rearranging the equation, we have 9y = 8x + 82. Divide both sides by 9 to solve for y: y = (8/9)x + 82/9. The slope of the given line is 8/9 and the perpendicular line will have a slope of -9/8. Now, we can use the point-slope form to find the equation of the perpendicular line.
Using the point-slope form, we have: y - y1 = m(x - x1). Plugging in the values of the given point (-8, -2) and the slope (-9/8), we have: y - (-2) = -9/8(x - (-8)). Simplifying the equation, we get: y + 2 = -9/8(x + 8). Finally, we can rearrange the equation into slope-intercept form to isolate y: y = -9/8x - 11/4. Therefore, the equation of the line perpendicular to -8x + 9y = 82 and passing through the point (-8, -2) in slope-intercept form is y = -9/8x - 11/4.