Question 224555
Write the slope intercept form of the equation of the line described.

through:(4,-4), parallel to y=-x-4


Step 1.  We can find the slope by recognizing that parallel lines have the same slope.  Since {{{y=-x-4}}} is in slope-intercept form given as y=mx+b where the slope m=-1 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=-1 going through point (4,-4).


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


Step 5.  Now we're given {{{m=1/3}}}.  Substituting above values and variables in the slope equation m yields the following steps:


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


{{{-1=(y-(-4))/(x-4)=(y+4)/(x-4)}}}


Step 6.  Multiply x-4 to both sides to get rid of denominator on right side of equation.


{{{-1(x-4)=y+4}}} 


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


Step 7  Subtract 4 from both sides of the equation


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


{{{-x=y}}}  

Step 8.  ANSWER:  The equation in slope-intercept form is {{{y=-x}}}



Note:  the above equation can be rewritten as 


{{{x+y=0}}}


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


*[invoke describe_linear_equation 1, 1, 0 ]


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