SOLUTION: Find the value of "a" if a line containing the point (a, -2a) has a y-intercept of 6 and slope of -2/3

Algebra ->  Linear-equations -> SOLUTION: Find the value of "a" if a line containing the point (a, -2a) has a y-intercept of 6 and slope of -2/3      Log On


   

Question 1089246: Find the value of "a" if a line containing the point (a, -2a) has a y-intercept of 6 and slope of -2/3
Answer by MathLover1(20849) About Me  (Show Source):
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find: the value of "a"
if a line: y=mx%2Bb where m is a slope and b is y-intercept

given:
has a y-intercept of 6 and
slope of -2%2F3
y=-%282%2F3%29x%2B6
containing the point (a, -2a) =(x, y)
-2a=-%282%2F3%29a%2B6 ........solve for a
-2a%2A3=-3%282%2F3%29a%2B6%2A3
-6a=-2a%2B18
-18=-2a%2B6a
-18=4a
-18%2F4=a
a=-9%2F2
and point is:(-9%2F2, -2%28-9%2F2%29)->(-9%2F2, 9)