SOLUTION: Given the following two linear equations, determine whether the lines are parallel, perpendicular, or neither. Show all work and explain your conclusion fully. 5x+4y=40 16x=15

Algebra ->  Linear-equations -> SOLUTION: Given the following two linear equations, determine whether the lines are parallel, perpendicular, or neither. Show all work and explain your conclusion fully. 5x+4y=40 16x=15      Log On


   

Question 1128884: Given the following two linear equations, determine whether the lines are parallel, perpendicular, or neither. Show all work and explain your conclusion fully.
5x+4y=40
16x=15+20y

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The key to the answer is finding the slope for the lines.
Solve each equation for y to find the slope-intercept form of each equation.
5x%2B4y=40 --> 4y=40-5x --> y=40%2F4-5x%2F4 --> y=%28-5%2F4%29x%2B10
16x=15%2B20y --> 16x-15=20y --> y=16x%2F20-15%2F20 --> y=%284%2F5%29x-3%2F4
we got different expressions for y, so the lines are not the same line in disguise.
The slopes (the coefficients of x) are -5%2F4 and 4%2F5 .
Their product is
%28-5%2F4%29%284%2F5%29=-1 .
The fact that the product is -1 means that the lines are perpendicular.