Question

Find the value of d so the line that passes through (a,b) and (c,d) has a slope of 1/2.

Answer 1

I'm guessing that in the book or the homework sheet, they gave you
the values of 'a', 'b', and 'c', and you're supposed to find the value of 'd'.

If you have two points on the line, then the slope of the line is

                       (the change in 'y') divided by (the change in 'x') .

If the two points are (a, b) and (c, d), then the slope of the line is

                       (d - b) divided by (c - a) ,

and you have to find the value of 'd' that makes that whole expression
equal to 1/2.

                                      (d - b) / (c - a) = 1/2

Multiply each side by  (c - a):     (d - b) = 1/2(c - a)

Add 'b' to each side:                    d        =  1/2(c - a)  +  b

If you know the values of 'a', 'b', and 'c', you can find the value of 'd'.