Question

write the equation of the line that is perpendicular to y = 7x - 3 and passes through the origin

Answer 1

Answer is 7y=-x for the question

Answer 2

For this case we have to by definition, if two lines are perpendicular when it is fulfilled that:

$m_ {1} * m_ {2} = - 1$

We have the following line:

$y = 7x-3$

So:

$m_ {1} = 7$

We find $m_ {2}:$

$m_ {2} = \frac {-1} {m_ {1}} = \frac {-1} {7} = - \frac {1} {7}$

Thus, the equation is of the form:

$y = - \frac {1} {7} x + b$

We find "b", taking into account that the line passes through the origin:

$0 = - \frac {1} {7} (0) + b\\b = 0$

Finally, the equation is:

$y = - \frac {1} {7} x$

Answer:

$y = - \frac {1} {7} x$