Answer:
(9/4)x - 47/4
Explanation:
To find the equation of line s, which is perpendicular to line r and passes through the point (3,5), you can follow these steps:
1. Determine the slope of line r: In the equation of line r, y = (-4/9)x - 2, the coefficient of x is the slope of the line. So, the slope of line r is -4/9.
2. Find the negative reciprocal of the slope of r to get the slope of s: Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of -4/9 is 9/4.
3. Use the point-slope form to write the equation of line s: You have the slope (m = 9/4) and a point (x1, y1) = (3, 5). The point-slope form of a line is given by:
y - y1 = m(x - x1)
Plug in the values:
y - 5 = (9/4)(x - 3)
Now, you can simplify and rearrange the equation:
y - 5 = (9/4)x - (9/4)(3)
y - 5 = (9/4)x - (27/4)
Add 5 to both sides to isolate y:
y = (9/4)x - (27/4) + 5
To make it a more common form, you can express 5 as 20/4:
y = (9/4)x - (27/4) + (20/4)
Now, combine the constants:
y = (9/4)x - (27/4 + 20/4)
y = (9/4)x - (47/4)
So, the equation of line s is:
y = (9/4)x - 47/4