330,340 views
43 votes
43 votes
Find the equation of the line that passes through (3,1) and is parallel to y=2x+3

User Kassie
by
2.9k points

1 Answer

11 votes
11 votes

Answer:

y -1 = 2(x -3)

Explanation:

The given equation is in slope-intercept form:

y = mx +b . . . . line with slope m and y-intercept b

y = 2x +3 . . . . . line with slope 2 and y-intercept 3

__

A parallel line will have the same slope. Since you are given a point, it is convenient to use the point-slope form for the equation you want:

y -k = m(x -h) . . . . . line with slope m through point (h, k)

y -1 = 2(x -3) . . . . . . line with slope 2 through point (3, 1)

__

Additional comment

If you want the slope-intercept form you can solve for y:

y = 2(x -3) +1 = 2x -6 +1

y = 2x -5 . . . . . slope-intercept form of the parallel line

User Rob J
by
2.0k points