Question 229265
How do you get an equation for a parallel line that passes through a given point?


example:  (3,4); y=2x-7


Step 1.  We note that parallel lines have the same slope.


Step 2.  The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept b at x=0 or point (0,b).  Here, the slope of the give line is m=2 since y=2x-7.  So now that we have the slope m=2, we need a line that has the same slope passing through (3,4)


Step 3.  The slope m is given as


{{{m=(y2-y1)/(x2-x1)}}}


Step 4.  Let (x1,y1)=(3,4) or x1=3 and y1=4.  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


Step 5.  Now we're given {{{m=2}}}.  Substituting above values and variables in the slope equation m yields the following steps:


{{{m=(y2-y1)/(x2-x1)}}}


{{{2=(y-4)/(x-3)}}}


Step 6.  Multiply (x-3) to both sides to get rid of denominators on both sides of equation.


{{{2(x-3)=cross(x-3)(y-4)/cross(x-3)}}} 


{{{2x-6=y-4}}} 


Step 7.  Now add 4to both sides of equation to solve for y.


{{{2x-6+4=y-4+4}}} 


{{{2x-2=y}}}



Step 8.  ANSWER:  The equation is {{{y=2x-2}}}


Here's a graph below and note the slope and y-intercept at x=0  or point (0, 2) and the x-intercept at y=0 or at point (51/3, 0)and note it is consistent with the equation when substituting these 


{{{graph(400,400, -5,5,-5,5, 2x-2)}}}


Note:  the above equation can be rewritten in standard form as 


{{{-2x+y=-2}}}


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J