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Find a equation to the straight line which passes through the point (-5,4) and is such that the portion of it between the axis is divided by the point in the ratio 1:2

Find a equation to the straight line which passes through the point (-5,4) and is such that the portion of it between the axis is divided by the point in the ratio 1:2

Grade:10

1 Answers

Aditya Gupta
2081 Points
2 years ago
Equation of line through point (−5,4) and slope m: y=4+m(x+5) 
y-intercept=(0,5m+4)  x-intercept=(−5m+4m,0)
Since (−5,4) divides line segment in the ratio 1:2, then y-coordinate 4 must be 1/3 or 2/3 of the way between 0 and 5m+4.
4=0+1((5m+4)−0)/3 ⟶ m=8/5  4=0+2((5m+4)−0)/3 ⟶ m=2/5
There are 2 lines such that the line segment between the 2 intercepts are divided in the ratio 1:2
they are
y=8x/5+12 and y=2x/5+6
or 8x−5y+60=0 and 2x−5y+30=0
kindly approve :)

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