anonymous
  • anonymous
Determine whether each pair of equations represents perpendicular lines y – x = 3 y = –x + 7
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
to check the prduct of the slopes should be -1
saifoo.khan
  • saifoo.khan
y - x = 3 y + x = 7 ======= 2y = 10 y = 5. Now substitute this value in the equation again to get the value for x.
anonymous
  • anonymous
how did you get the y= 5 though you add up the 7 and 3 to get 10 but how the 5 come along

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saifoo.khan
  • saifoo.khan
2y = 10 divide 2 from both sides, \[y = \frac{10}{2}\]\[y = 5\]
anonymous
  • anonymous
ok i see
anonymous
  • anonymous
so do i do the same for x
saifoo.khan
  • saifoo.khan
Now as you have the value for y. now insert in any equation to get the corresponding value of x.
myininaya
  • myininaya
Well we are suppose to see if the lines are perpendicular => you need to ask the question are the slopes opposite reciprocals?
saifoo.khan
  • saifoo.khan
oh man! im blind. Thanks @myininaya for saving the day.
myininaya
  • myininaya
=>if they are, we have perpendicular lines =>if they are not, we do not have such lines
myininaya
  • myininaya
Well unless we have horizontal and vertical lines going on together
myininaya
  • myininaya
But for this case we do not worry about that since we do not
myininaya
  • myininaya
Put both of these lines into y=mx+b form The first equation needs to be put in this form The second equation is already in this form
myininaya
  • myininaya
m is the slope
anonymous
  • anonymous
A plot is attached. The lines, y=x+3 in blue and y=-x+7 in red are perpendicular. A plot is not a proof, however, in the case of school book problems a plot is usually correct regarding mutual perpendicularity. Two lines are perpendicular if the coefficient of the x term of one line is equal to the negative of the reciprocal of the x coefficient of the other line. 1=-(1/-1) ?, 1=1 in this case so the lines are perpendicular.
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