Answer:
Therefore, the equation of the line perpendicular to y = 5/4x + 3/4 that passes through the point (-4, 9) is y = (-4/5)x + 23/5.
Explanation:
To find the equation of the line perpendicular to y = 5/4x + 3/4, we need to determine its slope. We know that the slope of a line perpendicular to this line will be the negative reciprocal of its slope.
The slope of y = 5/4x + 3/4 is 5/4, so the slope of the perpendicular line will be -4/5.
Now we can use the point-slope form of the equation of a line to find the equation of the perpendicular line that passes through the point (-4, 9):
y - y1 = m(x - x1)
Where m is the slope of the line and (x1, y1) is the given point.
Substituting in m = -4/5 and (x1, y1) = (-4, 9), we get:
y - 9 = (-4/5)(x + 4)
Expanding and simplifying, we get:
y = (-4/5)x + 23/5
Therefore, the equation of the line perpendicular to y = 5/4x + 3/4 that passes through the point (-4, 9) is y = (-4/5)x + 23/5.