Final answer:
The equation of the line passing through the point (-4, -11) and perpendicular to the given line is y = (5/4)x - 6. To find this, we first determined the slope of the given line, which is -4/5, and then found the negative reciprocal for the perpendicular line, which is 5/4. Finally, we used point-slope form to derive the equation of the new line, arriving at option B.
Step-by-step explanation:
To write an equation of a line passing through the point (-4, -11) and perpendicular to the line 4x + 5y = -45, we must first find the slope of the given line and then determine the slope of the line perpendicular to it.
The given line 4x + 5y = -45 can be written in slope-intercept form: y = mx + b, where m is the slope. We rearrange the given equation to find the slope of the given line:
- 5y = -4x - 45
- y = (-4/5)x - 9
The slope of the given line is -4/5, so the slope of a line perpendicular to it would be the negative reciprocal, which is 5/4.
Now, using the slope 5/4 and the point (-4, -11), we use the point-slope form of a line equation, which is y - y1 = m(x - x1), to find the equation of the new line:
- y - (-11) = (5/4)(x - (-4))
- y + 11 = (5/4)x + 5
- y = (5/4)x + 5 - 11
- y = (5/4)x - 6
Therefore, the equation of the line passing through the point (-4, -11) and perpendicular to the line 4x + 5y = -45 is y = (5/4)x - 6, which corresponds to option B.