1). what is an equation of the line that is perpendicular to y=−4/5x+3 and passes through the point (4, 12) ? 2). what is an equation of the line that is perpendicular to −x+3y=9 and passes through the point (−3, 2) ?

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.  and 12 = 5 + b.  b = 7.  So the equation you need is .  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 .  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. and 2 = 9+b so b = -7.  Our new equation then is y=-3x-7.  There you go!

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !