Question

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

Which of these is the equation of this line?
A = −6 B = 6 C = +6 D = − +6

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=(y_(2)-y_(1))/(x_(2)-x_(1))`

Substituting the values we get,

`m=(0-6)/(6-0)=(-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