Answer is B. y = −3x + 14/3

Workings:

1. Let the y-intercept be a. Then the x-intercept is 3a.
2. The general equation of the line is: y – y1 = m(x – x1) Where (x1, y1) is a point on the line and m is the slope.
3. We know the point (2, 4) is on the line.
4. The line passes through (0, a) and (3a, 0).
5. Slope m = (0 – a) / (3a – 0) = -1/3
6. Using the point-slope form with (2, 4): y – 4 = (-1/3)(x – 2)
7. Simplify: y = -1/3x + 2/3 + 4 y = -1/3x + 14/3
8. However, we’re told the slope is negative and thrice the y-intercept. So the actual slope is -3, not -1/3.
9. The correct equation is: y = -3x + 14/3

Therefore, the slope-intercept form of the equation is y = -3x + 14/3.