Question

Find the equation of line passing through the point (5,6) and making equal intercept on x & y axis​

Answer 1

Answer:

The equation of the required line is x+y-11=0

Step-by-step explanation:

$\text{concept:}$

$\text{The equation of the line in intercept form is }$

$\boxed{\bf\frac{x}{a}+\frac{y}{b}=1}$

Given:

x-intercept=y-intercept

a=b

The equation of the line becomes

$\frac{x}{a}+\frac{y}{a}=1$

$x+y=a$

since it passes through (5,6),

$5+6=a$

$\implies\bf\,a=11$

Therefore, the required line is

$x+y-11=0$

Answer 2

Answer:

Equation of the line is $y = -x + 11$

Step-by-step explanation:

Let a be the x and y-intercept of the line,

i.e. the line passes through the line (a, 0) and (0, a),

We know that,

The equation of the line passes through $(x_1, y_1)$ and $(x_2, y_2)$ is,

$y-y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1)$

So, the equation of the line would be,

$y - 0 =\frac{a-0}{0-a}(x-a)$

$y = -\frac{a}{a}(x-a)$

$y=-1(x-a)$

$y = -x + a$

If the line passes through (5, 6) then (5, 6) must satisfy the line,

$6 = -5 + a\implies a = 11$

Thus, the equation of the line would be,

$y = -x + 11$

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