A line makes positive intercepts on coordinate axes whose sum is 7 and it passes through (-3,7) find its equation.
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The Brain
apmpman
Apmpman Brainly Challenger
There could be multiple answers to this question.
x/a + y/b = 1
If we write the equation of a straight line in this form, then the x axis intercept is a and y axis intercept is b. Given a+b = 5
bx + a y = ab
(5 - a) x + a y = a (5 - a)
Point P (-3,4) lies on the straight line.
-3 (5-a) + 4 a = 5a - a²
-15 + 3a + 4a = 5a - a²
a² + 2a - 15 = 0
(a + 5)(a-3) = 0 a = -5 or 3
b = 10 or 2
So equations of the two straight lines are :
10 x - 5y = -50 or 2 x - y + 10 = 0 and 2 x + 3 y = 6
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we can also solve this question by using y = m x + c form where c is the y axis intercept and x axis intercept is -c/m.
c - c/m = 5
m c - c = 5m c = 5 m /(m-1)
4 = -3m+c
4 = - 3 m + 5 m /(m-1)
4 (m-1) = -3m(m-1) + 5 m
4 m - 4 = - 3 m² + 3m + 5m
3m² - 4m - 4 = 0
m = [4 +- √(16+48)]/6 = (4+- 8 )/ 6 = 2 or -4/6 or -2/3
c = 5 * 2/1 = 10 or (5*-2/3) / (-1-2/3) = 2
y = 2 x + 10 or y = - 2x /3+4
Answer:
x/a + y/b = 1
If we write the equation of a straight line in this form, then the x axis intercept is a and y axis intercept is b.
Given a+b = 5
bx + a y = ab
(5 - a) x + a y = a (5 - a)
Point P (-3,4) lies on the straight line.
-3 (5-a) + 4 a = 5a - a²
-15 + 3a + 4a = 5a - a²
a² + 2a - 15 = 0
(a + 5)(a-3) = 0
a = -5 or 3
b = 10 or 2
So equations of the two straight lines are :
10 x - 5y = -50 or 2 x - y + 10 = 0 and 2 x + 3 y = 6