Question

The graph of a line passes through the points (0, 6) and (6, 0).

Answer 1

The equation of line passing through (0, 6) and (6, 0) is y = -x + 6

Solution:

Given that graph of a line passes through the points (0, 6) and (6, 0)

The equation of line containing two points is given as:

$y - y_1 = m(x - x_1)$ ----- eqn 1

Where "m" is the slope of line

Here given two points are (0, 6) and (6, 0)

$(x_1 , y_1) = (0, 6)\\\\(x_2, y_2) = (6, 0)$

Let us first find the slope of line

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the values we get,

$m=\frac{0-6}{6-0}=\frac{-6}{6}=-1$

Thus slope of line "m" = -1

Substituting in eqn 1

$y - 6 = -1(x - 0)\\\\y - 6 = -x + 0\\\\y - 6 = -x\\\\y = -x + 6$

In standard form we get,

y = -x + 6

x + y = 6

Thus equation of line is found