Final answer:
The equation of the line perpendicular to 4x+5y=11 that passes through the point (-4, -2) is y = 5/4x + 3.
Step-by-step explanation:
To find the equation of the line perpendicular to 4x+5y=11 and passing through the point (-4, -2), we first need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope. For the given equation, 4x + 5y = 11, we can rewrite it in slope-intercept form:
5y = -4x + 11
y = (-4/5)x + 11/5
Therefore, the slope of the given line is -4/5. Perpendicular lines have slopes that are negative reciprocals of each other so the slope of the line we are seeking would be 5/4. Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we get:
y - (-2) = 5/4(x - (-4))
y + 2 = 5/4(x + 4)
The equation of the perpendicular line in point-slope form is y + 2 = 5/4(x + 4). To write this in slope-intercept form, we distribute and isolate y:
y = 5/4x + 5 - 2
y = 5/4x + 3
So, the slope-intercept form of the equation for the perpendicular line is y = 5/4x + 3.