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:
[tex]y - y_1 = m(x - x_1)[/tex] ----- eqn 1
Where "m" is the slope of line
Here given two points are (0, 6) and (6, 0)
[tex](x_1 , y_1) = (0, 6)\\\\(x_2, y_2) = (6, 0)[/tex]
Let us first find the slope of line
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Substituting the values we get,
[tex]m=\frac{0-6}{6-0}=\frac{-6}{6}=-1[/tex]
Thus slope of line "m" = -1
Substituting in eqn 1
[tex]y - 6 = -1(x - 0)\\\\y - 6 = -x + 0\\\\y - 6 = -x\\\\y = -x + 6[/tex]
In standard form we get,
y = -x + 6
x + y = 6
Thus equation of line is found
