Question 224826
Write the slope intercept form of the equation of the line through the given point with the given slope.

through:(3,-1), slope=-1


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=-1 going through point (3,-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)=(3,-1) or x1=3 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}}}.  Substituting above values and variables in the slope equation m yields the following steps:


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


{{{-1=(y-(-1))/(x-3)=(y+1)/(x-3)}}}


Step 6.  Multiply x-3 to both sides to get rid of denominator on right side of equation.


{{{-(x-3)=y+1}}} 


{{{-x+3=y+1}}} 


Step 7.  Add -1 to both sides of the equation


{{{-x+3+(-1)=y+1+(-1)}}} 


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


Step 7.  ANSWER:  The equation in slope-intercept form is {{{y=-x+2}}} where the slope m=-1 and the y-intercept b=2.


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


{{{x+y=2}}}


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


*[invoke describe_linear_equation 1, 1, 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