For 1.) if we need an equation of a line that is perpendicular to the one given, we will need the opposite reciprocal of the slope. The given slope is -4/5 so the opposite reciprocal is 5/4. If the line passes through (4, 12), we will use x=4 and y=12 to write a new equation that can be solved for b, the y-intercept. Here we go. [tex]12= \frac{5}{4}(4)+b [/tex] and 12 = 5 + b. b = 7. So the equation you need is [tex]y= \frac{5}{4}x+7 [/tex]. For 2.) we need to find the slope of the line since it's not apparent the way it is written. Solve it for y to find the slope. 3y=x+9 and [tex]y= \frac{1}{3}x+3 [/tex]. The slope is 1/3 so the opposite reciprocal is -3. That's the perpendicular slope. Using point (-3, 2) where x = -3 and y = 2, we will write the equation and solve for b. [tex]2=-3(-3)+b[/tex] and 2 = 9+b so b = -7. Our new equation then is y=-3x-7. There you go!
