Question 225449
Find the equation of the line that has a slope of -8 and passes through the point (-1,-5) write the equation in standard  form.


Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).  From the slope intercept form we can derive the standard form given as Ax+By=C where A, B, and C are constants.  Now, let's find the equation of the line in slope-intercept form


Step 2.  Here, we have to find the line with slope m=-8 going through point (-1,-5).


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)=(-1,-5) or x1=-1 and y1=-5.  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


Step 5.  Now we're given {{{m=-8}}}.  Substituting above values and variables in the slope equation m yields the following steps:


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


{{{-8=(y-(-5))/(x-(-1))=(y+5)/(x+1)}}}


Step 6.  Multiply x+1 to both sides to get rid of denominator on right side of equation.


{{{-8(x+1)=y+5}}} 


{{{-8x-8=y+5}}} 


Step 7.  Add -5 to both sides of the equation


{{{-8x-8+(-5)=y+5+(-5)}}} 


{{{-8x-13=y}}} 


Step 7.  The equation in slope-intercept form is {{{y=-8x-13}}} where the slope m=-8 and the y-intercept b=-13.


Note:  the above equation can be rewritten in standard form by adding 8x to both sides of the equation.


{{{-8x-13+8x=y+8x}}}


{{{8x+y=-13}}}   


Step 8.  ANSWER:  The equation of the line in standard form is {{{8x+y=-13}}}.   



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


{{{graph(600,600,-10,10,-20,10,-8x-13)}}}


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