Algebra 2 honors

Question

How do you get an equation from f(4)=-2 and f(-2)=4?

Answer 1

(4,-2) and (-2,4) are two points on the line (x,y) = (x, f(x))

the line has slope = "rise over run" = difference in y coordinates divided by the corresponding difference in x coordinates = (4--2)/(-2-4) = 6/-6 = -1 = (y-4)/(x+2)

y-4 = -x-2

y = -x+2 in slope intercept form

x+y= 2 is the equation in standard form

(assuming you wanted a linear equation Otherwise there are endless quadratic, cubic or higher degree equations that fit the given information)