Final answer:
The equation for the line that is perpendicular to -5x + 4y = -12 and passes through (5, -11) is 4x + 5y = -45.
Step-by-step explanation:
To find the equation of a line that is perpendicular to -5x + 4y = -12 and passes through (5, -11), we first need to determine the slope of the given line. The equation is in the form Ax + By = C, where A = -5, B = 4, and C = -12. The slope of the line is -A/B, so the slope of the given line is -(-5)/4 = 5/4.
Since the line we are looking for is perpendicular to the given line, its slope will be the negative reciprocal of 5/4. The negative reciprocal of 5/4 is -4/5.
So, the slope of the line we are looking for is -4/5.
Now that we know the slope of the line we are looking for, we can use the point-slope form of a line to find its equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Plugging in the values (5, -11) for (x1, y1) and -4/5 for m, we get y - (-11) = -4/5(x - 5), which simplifies to y + 11 = -4/5x + 20/5.
Rearranging the equation, we get 4/5x + y = -9, which can be written in standard form as 4x + 5y = -45.
Therefore, the equation for the line that is perpendicular to -5x + 4y = -12 and passes through (5, -11) is 4x + 5y = -45.