Final answer:
To find the equation of the line that is perpendicular to the given line, rearrange the given equation in the slope-intercept form. Determine the slope of the given line, and then find the negative reciprocal to get the slope of the perpendicular line. Finally, use the point-slope form with the given point and the perpendicular slope to find the equation of the line.
Step-by-step explanation:
To find the equation of the line that is perpendicular to the given line, we need to determine the slope of the given line first. Let's rearrange the given equation:
2(y + x) - 36x - y = -4
2y + 2x - 36x - y = -4
y - 34x = -4
Comparing this equation to the slope-intercept form (y = mx + b), we can see that the slope is -34.
To find the slope of the line perpendicular to it, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line would be the negative reciprocal of -34, which is 1/34.
Now, we can use the point-slope form (y - y1 = m(x - x1)) with the given point (-9, -10) and the slope 1/34 to find the equation of the perpendicular line:
y - (-10) = (1/34)(x - (-9))
y + 10 = (1/34)(x + 9)
y = (1/34)x + (1/34) * 9 - 10
y = (1/34)x + 9/34 - 340/34
y = (1/34)x - 331/34
This is the equation of the line that passes through the given point and is perpendicular to the given line.