Question 1147615: The equation for line j can be written as y=2x + 8. Another like k is perpendicular to line j and passes through the point (6,-6). Choose the equation for like k
A. Y= 1/2x-3
B. Y= -1/2x-3
C. Y=-2x-3
D. Y=-3/2x + 3
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! formula for line j is y = 2x + 8
line k is perpendicular to line j.
it will therefore have a slope that is a negative reciprocal to the slope of line j.
the general formula for line k is therefore y = -1/2 * x + b
since line k passes through the point (6,-6), then use that point to find the value of b.
replace x with 6 and y with -6 in the equation of y = -1/2 * x + b to get:
-6 = -1/2 * 6 + b
simplify to get:
-6 = -3 + b
solve for b to get:
b = -6 + 3 = -3
the equation of line k is therefore y = -1/2 * x - 3
here's the graph.you can see that the point (6,-6) is on that line, as well as see that the lines do indeed look perpendicular to each other.
line j is the red line.
line k is the blue line.
y-intercept for line j is 8, as it should be.
y-intercept for line k is -3, as it should be.
intersection of line j and k is at the point (-4.4,-.8)
line k passes through the point (6,-6), as it should.
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