What is the function rule for these ordered pairs (-2, 10) (-1, -7) (0, -4) (1, -1) (2, 2)?

1 Answer
May 30, 2016

#color(blue)("So the function rule is "y=3x-4)#

Explanation:

Given:
#y-> 10;-7;-4;-1;2#
#x->-2;-1;0;1;2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Assumption: the question has an error. The +10 should be -10

Thus we have

#y_2-y_1 -> -7-(-10) = +10-7 = +3#

#"-10 -7 -4 -1 2"#
#" \/"color(white)(.)"\ /"color(white)(.)"\/"color(white)(.)"\/"#
#" 3 3 3 3 " larr " difference in "y" (increasing)"#

#"-2 -1 0 1 2"#
#" \/"color(white)(.)"\ /"color(white)(.)"\/"color(white)(.)"\/"#
#" 1 1 1 1 " larr " difference in "x" (increasing")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the standard form equation of a straight line:
#" "y=mx+c#

where m is the gradient #->( "change in y")/("change in x") -> (+3)/(+1)=+3#

#y=3x+c#

Take any given point #P->(x,y)" " -> (-1,-7)#

Then #y=3x+c" " ->" "-7=3(-1)+c#

#=> c = 3-7=-4#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("So the function rule is "y=3x-4) #

Tony B