Math help with problem

Question

If k(x) is a linear function, where k(−5)=2, and k(1)=1, determine the slope-intercept equation for k(x), then find k(-2).

The equation of the line is: 

k(-2) =

f r(x) is a linear function, where r(−3)=4, and r(5)=2, determine the slope-intercept equation for r(x), then find r(4).

The equation of the line is:

r(4) = 

Answer 1

line through (-5,2) and (1,1) is

y-1= m(x-1) where m=(1-2)/(1+5) =-1/6

y = (-1/6)x +1/6+1

y =k(x)= (-1/6)x +7/6 in slope intercept form

or

6y=-x+7

x+6y=7 in standard form

k(-2) =9/6= 3/2

(-3,4), (5,2) have a line with equation

y-2 = m(x-5) where m=(2-4)/(5+3) = -2/8= -1/4

y-2 =(-1/4)(x-5) =(-1/4)x+5/4

y = r(x) = (-1/4)x +13/4 in slope intercept form

or

4y=-x+13

x+4y=13 in standard form

r(4) =-1+13/4 = 9/4