Final answer:
The equation of line v, which is perpendicular to line u with the equation y = -(9/4)x + 1 and passes through the point (-3, 2), is y = (4/9)x + 10/3.
Step-by-step explanation:
To find the equation of line v that is perpendicular to line u with the equation y = -(9/4)x + 1, we need to determine the slope of line v. The slope m of line u is -(9/4), which means that the slope of line v will be the negative reciprocal, since perpendicular lines have slopes that are negative reciprocals of each other. Hence, the slope of line v is 4/9. Using the point-slope form y - y1 = m(x - x1), where (x1, y1) is the point (-3, 2) on line v, and plugging in the slope and the point, we get:
y - 2 = (4/9)(x - (-3))
Expanding the equation, we get:
y - 2 = (4/9)(x + 3)
Multiplying both sides by 9 to clear the fraction, and then distributing the 4, we get:
9y - 18 = 4x + 12
Finally, to write the equation in slope-intercept form y = mx + b, we get:
y = (4/9)x + (18 + 12)/9
y = (4/9)x + 30/9
y = (4/9)x + 10/3
So, the equation of line v is y = (4/9)x + 10/3.