Question

Use the intercept form to find the general form of the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts

(a, 0) and (0,b) is x/a + y/b = 1, a ≠ 0, b ≠ 0
x-intercept (-1/6, 0)
y-intercept (0, -2/3)

Answer 1

To find the general form of the equation of the line with the given intercepts
`\((a, 0) = \left(-(1)/(6), 0\right)\) and \((0, b) = \left(0, -(2)/(3)\right)\)`, we'll start with the intercept form:

`\[(x)/(a) + (y)/(b) = 1\]`

Substituting the given values
`\(a = -(1)/(6)\) and \(b = -(2)/(3)\)`, we get:

`\[-(x)/((1)/(6)) - (y)/((2)/(3)) = 1\]`

To eliminate the fractions, we'll multiply both sides of the equation by
`\(-6 * -3\)`:

`\[(-6 * -3) * (x)/(-1/6) + (-6 * -3) * (y)/(-2/3) = (-6 * -3) * 1\]`

Simplifying, we get:

`\[-2x - 9y = -18\]`

This is the general form
`\(Ax + By + C = 0\)` of the line, with
`\(A = -2\), \(B = -9\), and \(C = -18\)`.