a line through (-1,b) and (c,8) is parallel to a line through (-6,3) and (0,12)

Answer 1

The slope of the line through (-6,3) and (0,12) is 9/6 = 3/2. The line through the first pair of points must have the same slope.

Any pair of points which maintains this relationship will work. One example is (-1,5) and (1,8), because the vertical change is 3 and the horizontal change is 2. (-1,-22) and (19,8) will also work, as will (-1,23) and (-11,8). Any numbers will work as long as the following relationship is maintained for any value of x ...

c = x - 1

b = 8 - 3/2 x

Answer 2

parallel lines have the same slope, so first find the slope of the line you have information for....

9/6 = 3/2 as a slope

using the equation of the line we can get our original line as

y = 3/2x + 12

now use your two new points to find b and c

b = 21/2

c = -8/3