or The equation for line r can be written as y= – 4 9 x–2. Line s is perpendicular to line r and passes through (3,5). What is the equation of line s?

Answer 1

if r is y=-(4/9)x -2

then a perpendicular line s has a negative inverse slope = 9/4

y=9x/4 + b

to find b plug in the point,x=3, y=5

5 = 9(3)/4 + b

b = 5-27/4 = -7/4

y= 9x/4 - 7/4 is line s in slope intercept form

or

9x -4y = 7 in standard form

Answer 2

Because of the way your question is written, I'll assume that the equation of line r is y = (-4/9)x - 2.

The line perpendicular to this will have a negative, reciprocal slope to the given line. Since the given line has a slope of -4/9, the slope of any line that's perpendicular to it will have a slope of 9/4.

From there, you can use the point-slope equation: y = m(x - x₁) + y₁. Use the given point (3,5) as (x₁,y₁) and m=9/4. So, y = (9/4)(x - 3) + 5. You can leave this as is for the equation of line s, or distribute the 9/4 and simplify to put the equation into slope-intercept form.

Hope this helps!!