Question

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

Answer 1

Answer:

  y -1 = 2(x -3)

Step-by-step 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

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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)

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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