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Question 169116: Find an equation for the line with the given property.
a.) It passes through the point (3,-6) and is parallel to the line 3x+y-10=0
b.) It has the x-intercept 6 and the y-intercept 4.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find an equation for the line with the given property.
a.) It passes through the point (3,-6) and is parallel to the line 3x+y-10=0
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Find the slope, m, of the line
Put the eqn into slope-intercept form, y = mx + b
3x+y-10=0
y = -3x+10
So the slope is -3
Parallel means the slope is the same.
then,
y-y1 = m*(x-x1) (x1,y1) is the point (3,-6)
y-(-6) = -3*(x-3)
y+6 = -3x+9
y = -3x+3 (slope-intercept form)
3x+y = 3 (standard form)
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b.) It has the x-intercept 6 and the y-intercept 4.
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at the x-intercept, y = 0
at the y-intercept, x = 0
So that's 2 points, (0,4) and (6,0)
The slope of the line thru those is:
(y2-y1)/(x2-x1)
m = (0-4)/(6-0)
m = -2/3
Then use either point:
y-y1 = m*(x-x1)
y-0 = (-2/3)*(x-6)
y = -2x/3 + 2 (SI form)
2x + 3y = 6 (standard form)
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