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