Question

A line makes positive intercepts on coordinate axes whose sum is 7 and it passes through (-3,7) find its equation.​

Answer 1

$\huge\mathcal{Solution}$

Answers

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 2

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