Question 224557
Write the slope intercept form of the equation of the line described.

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


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


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


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)=(-2,4) or x1=-2 and y1=4.  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


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


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


{{{-5/2=(y-4)/(x-(-2))=(y-4)/(x+2)}}}


Step 6.  Multiply x+2 to both sides to get rid of denominator on right side of equation.


{{{-5(x+2)/2=y-4}}} 


{{{-5x/2-5=y-4}}} 


Step 7.  Add 4 to both sides of the equation


{{{-5x/2-5+4=y-4+4}}}


{{{-5x/2-1=y}}}


Step 7.  ANSWER:  The equation in slope-intercept form is {{{y=-5x/2-1}}}



Note:  the above equation can be rewritten as 


{{{5x+2y=-2}}}


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


*[invoke describe_linear_equation 5, 2, -2 ]


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