Area is 1/2 the product of the x and y intercepts.
An equation of a straight line with negative slope and positive y intercept,
can be rearranged in the form:
x/a + y/b = 1
where a is the x-intercept and b the y-intercept (and both a and b are positive).
Now, the triangle made by the x- and y- axes and the above straight line
is right-angled with base a and altitude b, and so has area:
a b/2.
The line y = -2 x + 6 rearranged in 2-intercept form is:
x/3 + y/6 = 1.
So a = 3, b = 6 and area
a b / 2 = 9.