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How do you find a line parallel to y=2x+3

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2 Answers

The pattern of this equation may look familiar to you... remember y=mx+b?  Called the slope-intercept form, because the cooefficient (multiplier) for x, represented by the letter m, is the "slope", or tilt, of the line on an x-y graph.  The b represents where the equation line intercepts (crosses) the y-axis (the "intercept") when x=0.  In your equation, m = the slope = +2, and the y-axis intercept = +3.  Plug in a few values for x, solve for y, then plot the results (x and y) on your graph...  If you set x=0, then you can easily see that y=2(0)+3 = +3, or that the line crosses the vertical y-axis at x=0 when y=+3.  So there's one point for your line:  (0,+3) (the first coordinate listed is the x coordinate, and the second one is the y-coordinate).  

Any line parallel to that equation line (they never touch and remain the same distance apart, no matter how long) has the same tilt, or slope, so any other similar equation with an m = 2 will be parallel.  Good luck!

Margaux,

The customary form of a straight line is:

y=m*x + b  where m is the line slope ( Δy/ Δx ) and b is the y intercept ( b = f(x=0)

Your line, y=2*x + 3, has a slope of 2.   Any straight line with a slope of 2 is parallel to your line.

Example:   y =  2*x + 7  is parallel (and above your line because the intercept is 7).

Good Luck!  BruceS