# find an equation of a line through the given point and parallel to and perpendicular to y=2x+1 at (3,1)

Asked on by tarfa123

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given `y=2x+1` , find the equation of a line parallel to this line that goes through the point (3,1).

(1) Parallel lines have the same slope.

(2) The slope of the given line is 2. (It is in slope-intercept form; `y=mx+b` where m is the slope and b is the y-intercept.)

(3) Thus the required line has slope 2 and contains the point (3,1). We use the point-slope form of a line:

Given slope m and a point `(x_1,y_1)` the equation of a line is:

`y-y_1=m(x-x_1)`

So we have `y-1=2(x-3)`

or in slope-intercept form we get `y=2x-5`

** If you know a point and the slope an alternative is to plug directly into the slope-intercept form and solve for the intercept:

We know m=2 and that when y=1,x=3 so

`1=2(3)+b=>b=-5` so we get y=2x-5 as above.

We’ve answered 319,199 questions. We can answer yours, too.