SOLUTION: without graphing,tell whether the graphs of the equations are parallel, perpendicular, or neither. justify your answers using complete sentences. m(x)= -5x + 123/7 and x+5y= -12

Algebra ->  Rational-functions -> SOLUTION: without graphing,tell whether the graphs of the equations are parallel, perpendicular, or neither. justify your answers using complete sentences. m(x)= -5x + 123/7 and x+5y= -12       Log On


   

Question 735628: without graphing,tell whether the graphs of the equations are parallel, perpendicular, or neither. justify your answers using complete sentences. m(x)= -5x + 123/7 and x+5y= -12
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
m%28x%29=+-5x+%2B+123%2F7 and x%2B5y=+-12+
firs write them in slope-intercept form: y=mx%2Bb where m=slope and b=y-intercept
m%28x%29=+-5x+%2B+123%2F7..already in slope-intercept form: m=-5 and b=+123%2F7

x%2B5y=+-12+...solve for y
5y=+-x-12+
y=+%28-1%2F5%29x-12%2F5+ ....m=-1%2F5 and b=+12%2F5
take a look at slopes: m=-5 and m=-1%2F5
lines that are parallel have same slope: since -5%3C%3E-1%2F5, these line are not parallel
to be perpendicular, lines have to have slopes negative reciprocals of each other
as you can see, 5 and 1%2F5 are reciprocals, but you have -5 and -1%2F5; so, since both negative, one is not negative reciprocal of other one
therefore,these line are not perpendicular ether
so, these lines are neither parallel nor perpendicular, they must be intersecting in one point
let's check it on a graph: