Question

Find the equation of a line which passes through point 3,4 and sum of its intercepts on the axis is 14

Answer 1

I believe the answer is y=2x+14. The formula is y=mx+b. m= slope b= y-intercept If this answer is the best answer, please mark it as the Brainliest. Thanks!

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

Intercept by x and y axis be a & (14 - a)

Hence,

${\boxed{\sf\:{Equation=\dfrac{x}{a}+\dfrac{y}{14-a}=1}}}$

$\textbf{\underline{Passes\;through\;(3,4)}}$

${\boxed{\sf\:{\dfrac{3}{a}+\dfrac{4}{14-a}=1}}}$

3(14 - a) + 4a = a(14 - a)

a² - 13a + 42 = 0

(a - 6)(a - 7) = 0

a = 6 also a = 7

Then,

a = b

b = 14 - 6 = 8

Also,

a = 7

b = 14 - 7 = 7

$\Large{\boxed{\sf\:{Equation=\dfrac{x}{6}+\dfrac{y}{8}=1}}}$

$\Large{\boxed{\sf\:{Equation=\dfrac{y}{7}+\dfrac{y}{7}=1}}}$

4x + 3y - 24 = 0

x + y - 7 = 0