Question 225969
Find the equation of the line containing the point (8, –39) and parallel to the line 6x+y= -4 .


Step 1.  We can find the slope by recognizing that parallel lines have the same slope.  So we need to put the equation of the line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept b when x=0 or at point (0,b). 

We can transform the given equation {{{6x+y=-4}}} by subtracting -6x from both sides of the equation


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


Since {{{y=-6x-4}}} is in slope-intercept form given as y=mx+b where the slope m=-6 and the y-intercept b=-4 when x=0 or at point (0,b) or (0,-4).


Step 2.  Now we have to find the line with slope m=-6 going through point (8,-39).


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)=(8,-39) or x1=8 and y1=-39.  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


Step 5.  Now we're given {{{m=-6}}}.  Substituting above values and variables in the slope equation m yields the following steps:


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


{{{-6=(y-(-39))/(x-8)=(y+39)/(x-8)}}}


Step 6.  Multiply x-8 to both sides to get rid of denominator on right side of equation.


{{{-6(x-8)/3=y+39}}} 


{{{-6x+48=y+39}}}


Subtract 39 from both sides of the equation


{{{-6x+48-39=y+39-39}}}


{{{-6x+9=y}}}


Step 7.  ANSWER:  The equation in slope-intercept form is {{{y=-6x+9}}}



Note:  the above equation can be rewritten as 


{{{6x+y=9}}}


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


*[invoke describe_linear_equation 6, 1, 9 ]


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