finding linear equation of the line that goes through the given points: f(4)=-5 and f(12)=1

Answer 1

(4,-5) and (12,1) are point on a line with slope = (1--5)/(12-4) = 6/8 = 3/4

using point slope equation

y-1 = (3/4)(x-12)

4y-4 = 3x -36

3x - 4y = 32

Answer 2

4 is the input x-value, when x=4, the output is -5

Dear Friend:

4 and 12 are inputs of the function:

 when x=4, the output is -5

when x=12, the output is 1

therefore, we can get an ordered pair

step 1: write the input and output as an ordered pair:

(4, -5) (12, 1)

step 2: find the slope:

m= “change y”

    "change x”

m= 1- (-5) =-6= 6 = 3 so m= 3/4

     2- 4   8 8 4

step: 3: use point slope intercept form: (be sure to leave answer in slope intercept form:

y= mx +b as your final answer:

y- y1 = m(x - x1) m=3/4 Pick point (12, 1)

y -1 = 3/4(x - 12)

y - 1 = 3/4x -36/4

y - 1 = 3/4x -9

 +1 +1

y =  3/4x -8

m= 3/4 and b=-8

I hope this helps!