Question 225964
Point (1, –2) , m = –5.


I assume you want to write the slope intercept form of the equation of the line through the given point (1,-2) with the given slope m=-5.


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).


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


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,-2) or x1=1 and y1=-2.  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-(-2))/(x-1)=(y+2)/(x-1)}}}


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


{{{-5(x-1)=y+2}}} 


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


Step 7.  Add -2 to both sides of the equation


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


{{{-5x+3=y}}} 


Step 7.  ANSWER:  The equation in slope-intercept form is {{{y=-5x+3}}} where the slope m=7 and the y-intercept b=-5.


Note:  the above equation can be rewritten in standard form as


{{{5x+y=+3}}}


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


*[invoke describe_linear_equation 5, 1, 3 ]


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