Question 226304
What is the equation for a line that contains the points (0,4) and is parallel to y=2x+3?


Step 1.  We can find the slope by recognizing that parallel lines have the same slope.  Since {{{y=2x+3}}} is in slope-intercept form given as y=mx+b where the slope m=2 and the y-intercept b=3 when x=0 or at point (0,b) or (0,3).


Step 2.  Now we have to find the line with slope m=2 going through point (0,4).


But the point (0,4) is the y-intercept.  Then y=2x+4.  


The next sequence of steps will show the same equation but this method is applicable even when the point is not the y-intercept.


Step 3.  Given two points (x1,y1) and (x2,y2), then the slope m is given as


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


Step 4.  Let (x1,y1)=(0,4) or x1=2 and y1=0.  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-0)=(y-4)/x}}}


Step 6.  Multiply x to both sides to get rid of denominator on right side of equation.


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


{{{2x=y-4}}} and after adding 4 to both sides yields {{{y=2x+4}}} same result as before.


Step 7.  ANSWER:  The equation in slope-intercept form is {{{y=2x+4}}}



Note:  the above equation can be rewritten as 


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


And the graph is shown below which is consistent with the above steps.


*[invoke describe_linear_equation -2, 1, 4 ]


I hope the above steps and explanation were helpful.


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And good luck in your studies!


Respectfully,
Dr J

http://www.FreedomUniversity.TV