Question

Determine whether each pair of equations represents perpendicular lines
y – x = 3 y = –x + 7

Answer 1

to check the prduct of the slopes should be -1

Answer 2

y - x = 3

y + x = 7
=======

2y = 10

y = 5.

Now substitute this value in the equation again to get the value for x.

Answer 3

how did you get the y= 5 though you add up the 7 and 3 to get 10 but how the 5 come along

Answer 4

2y = 10

divide 2 from both sides,
\[y = \frac{10}{2}\]\[y = 5\]

Answer 5

ok i see

Answer 6

so do i do the same for x

Answer 7

Now as you have the value for y.
now insert in any equation to get the corresponding value of x.

Answer 8

Well we are suppose to see if the lines are perpendicular
=>
you need to ask the question are the slopes opposite reciprocals?

Answer 9

oh man! im blind.
Thanks @myininaya for saving the day.

Answer 10

=>if they are, we have perpendicular lines
=>if they are not, we do not have such lines

Answer 11

Well unless we have horizontal and vertical lines going on together

Answer 12

But for this case we do not worry about that since we do not

Answer 13

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

Answer 14

m is the slope

Answer 15

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.