Question 224558
Write the slope intercept form of the equation of the line described.

through (-4,-1) parallel to y=-1x/2-1


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


Step 2.  Now we have to find the line with slope m=-1/2 going through point (-4,-1).


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,-1) or x1=-4 and y1=-1.  Let other point be ((x2,y2)=(x,y) or x2=x and y2=y.


Step 5.  Now we're given {{{m=-1/2}}}.  Substituting above values and variables in the slope equation m yields the following steps:


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


{{{-1/2=(y-(-1))/(x-(-4))=(y+1)/(x+4)}}}


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


{{{-1(x+4)/2=y+1}}} 


{{{-1x/2-2=y+1}}} 


{{{-1x/2-2=y+1}}}


Step 7.  Now subtract 1 form both sides of equation to solve for y.


{{{-x/2-2-1=y+1-1}}}


{{{-x/2-3=y}}}


Step 8.  ANSWER:  The equation in slope-intercept form is {{{y=-x/2-3}}}


Note: the above equation can be rewritten as 


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


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


*[invoke describe_linear_equation 1, 2, -6 ]



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