SOLUTION: The following equation represents the line that passes through (2h, h+1) and (h+3, 0) and has a slope of -3. What is the missing value in the equation? y + ____ = -3 (x - 7)

Algebra ->  Expressions-with-variables -> SOLUTION: The following equation represents the line that passes through (2h, h+1) and (h+3, 0) and has a slope of -3. What is the missing value in the equation? y + ____ = -3 (x - 7)      Log On


   

Question 1000193: The following equation represents the line that passes through (2h, h+1) and (h+3, 0) and has a slope of -3. What is the missing value in the equation?
y + ____ = -3 (x - 7)
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
REPORTED SOLUTION HERE WAS A MISTAKE,... NOW IS CORRECTED.

Try putting the equation into slope intercept form.
y%2Bw=-3%28x-7%29 and you do not know the value of w.
y=-3x%2B21-w

Look back to your given points and the known slope.
%28h%2B1-0%29%2F%282h-%28h%2B3%29%29=-3
%28h%2B1%29%2F%28h-3%29=-3
h%2B1=-3%28h-3%29
h%2B1=-3h%2B3--------MISTAKE FOUND HERE.
cross%284h%2B1=3%29,cross%284h=2%29,highlight%28cross%28h=1%2F2%29%29 and the two given points are (1,3/2) and ( 7/2,0).
h%2B1=-3h%2B9
h%2B3h%2B1=9
4h=9-1
4h=8
highlight%28h=2%29

EVALUATE THE GIVEN POINTS NOW ACCORDING TO h=2.
These Points are (4,3) and (5,0).


Using the known slope, and either of the given points, find the equation of the line.
cross%28y-0=-3%28x-7%2F2%29%29-----point-slope form,cross%28y=-3%28x-7%2F2%29%29
highlight%28cross%28y=-3x%2B21%2F2%29%29------The line wanted, but you want the unknown value w to be solved.
y-0=-3%28x-5%29
y=-3x%2B15

Compare the equivalent equations:
cross%28system%28y=-3x%2B21-w%2Cy-3x%2B21%2F2%29%29
system%28y=-3x%2B21-w%2Cy=-3x%2B15%29----both of these being slope-intercept form, but using the same w as earlier used.

The y-intercepts must be equal.
cross%2821-w=21%2F2%29,cross%2821-21%2F2=w%29,cross%28w=42%2F2-21%2F2%29,highlight%28highlight%28cross%28w=21%2F2%29%29%29
21-w=15
21-15=w
highlight%28highlight%28w=6%29%29-------The missing value in the blank in the requested point-slope equation given.

(Earlier mistake is now corrected).