Question 224552
Write the slope intercept form of the equation of the line described.

through:(-1,4), parallel to y=-5x+2


Step 1.  We can find the slope by recognizing that parallel lines have the same slope.  Since {{{y=-5x+2}}} is in slope-intercept form given as y=mx+b where the slope m=-5 and the y-intercept b=2 when x=0 or at point (0,b) or (0,2).


Step 2.  Now we have to find the line with slope m=-5 going through point (-1,4).


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


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


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


{{{-5=(y-4)/(x-(-1))=(y-4)/(x+1))}}}


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


{{{-5(x+1)=y-4}}} 


{{{-5x-5=y-4}}} 


Step 7.  Add 4 to both sides of the equation


{{{-5x-5+4=y-4+4}}}


{{{-5x-1=y}}}


Step 7.  ANSWER:  The equation in slope-intercept form is {{{y=-5x-1}}}



Note:  the above equation can be rewritten as 


{{{5x+y=-1}}}


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


*[invoke describe_linear_equation 5, 1, -1 ]


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