perpendicular 3 3.4 22

Question

Find an equation of the line that passes through
(2,7)
and is perpendicular to
y=2x−5.

Answer 1

1) What is the slope of the "reference" line (to which your line will be perpendicular)?  It's right their in the reference line's given equation.

 

2) So what must be the slope of the line perpendicular to the 'reference" line?  No doubt your book and/or teacher have mentioned a basic principle of slopes of any two perpendicular lines (other than one being horizontal, the other being vertical, which is a separate case).

 

3)  After carefully applying the above two strong hint, you will have a point on the perpendicular line (it's given) and the slope of the perpendicular line.  That is, you have point & slope so you may plug in your specific values into the equation

y-y₁ = m(x - x₁).

 

Done! (You may wish to use algebra skills to put the equation into some other well known form, afterwards)

Answer 2

Jessica,

 

The slope of the line which was given is m = 2. Any perpendicular line has its slope the negative reciprocal of 2, or −½.

 

Use the point-slope form of a line to get an equation for the perpendicular line:

 

y − 7 = −½(x − 2).

 

This is an equation. If you need another form of it, such as standard or slope-intercept form, you must simplify and rewrite it in that form.