Question 218283
Find m and b in f(x)=mx+b such that f(2)=2 and f(-2)= -2.


Step 1.  We can interpret f(2)=2 as a point (2,2) and f(-2)=-2 as a point (-2,-2)


Step 2.  The slope of the line m is given as


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


where for our example is x1=-2, y1=-2, x2=2 and y2=2 (think of {{{slope=rise/run}}}).  You can choose the points the other way around but be consistent with the x and y coordinates.  You will get the same result.


Step 3.  Substituting the above values in the slope equation gives


{{{m=(2-(-2))/(2-(-2))}}}


{{{m=4/4}}}


{{{m=1}}}


Step 4.  The slope is calculated as 1 or m=1


Step 5.  Now use the slope equation of step 1 and choose one of the given points.  I'll choose point (-2,-2).   Letting y=y2 and x=x2 and substituting m=1 in the slope equation given as,


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



{{{ 1=(y-(-2))/(x-(-2))}}}


{{{ 1=(y+2)/(x+2)}}}


Step 6.  Multiply both sides of equation by x+2 to get rid of denomination found on the right side of the equation



{{{ 1(x+2)=(x+2)(y+2)/(x+2)}}}



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



Step 7.  Now simplify and put the above equation into slope-intercept form.


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


Subtract 2 from both sides of the equation


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


{{{x=y}}}


Step 8.  See if the other point (2,2) or x=2 and y0intercept b=0 satisfies this equation


{{{y=x}}}


{{{2=2}}} which is a true statement.


  So the point (2,2) satisfies the equation and is on the line.  In other words, you can use the other point to check your work.


Note;  above equation can be also be transform into standard form as


{{{-x+y=0}}}


See graph below to check the above steps.


{{{graph(400,400, -5, 5, -5, 5, x)}}}


Step 9.  ANSWER:  {{{y=x}}} is in slope-intercept form where m=1 and y-intercept b=0


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J