Question

write an equation for the line perpendicular to y=2x-5 through the point (8,-2)

Answer 1

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

By definition, if two lines are perpendicular then the product of their slopes is -1.

We have the following equation of the line:

$y = 2x-5$

Then $m_ {1} = 2$

We find $m_ {2}:$

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

Thus, the perpendicular line will be of the form:

$y = - \frac {1} {2} x + b$

We substitute the given point and find "b":

$-2 = - \frac {1} {2} (8) + b$

$-2 = -4 + b\\-2 + 4 = b\\b = 2$

Finally, the equation is of the form:

$y = - \frac {1} {2} x + 2$

ANswer:

$y = - \frac {1} {2} x + 2$