Question

Please help ASAP!!

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) ?

Answer 1

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.
`12= (5)/(4)(4)+b` and 12 = 5 + b. b = 7. So the equation you need is
`y= (5)/(4)x+7`. 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
`y= (1)/(3)x+3`. 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.
`2=-3(-3)+b` and 2 = 9+b so b = -7. Our new equation then is y=-3x-7. There you go!