Answer:

The equation of a line in the xy-plane with x and y intercepts as 3 and 1, respectively, can be written in the form:

\[ \frac{x}{3} + \frac{y}{1} = 1 \]

Multiplying through by 3 to eliminate fractions:

\[ x + 3y = 3 \]

Now, to find the image of the point (-1,-4) in the line, you can use the formula for reflection of a point across a line. The reflection of a point (x, y) in the line Ax + By + C = 0 is given by:

\[ \left( x', y' \right) = \left( x - \frac{2Ax + 2By + 2C}{A^2 + B^2}, y - \frac{2Ax + 2By + 2C}{A^2 + B^2} \right) \]

For the line x + 3y - 3 = 0, A = 1, B = 3, and C = -3. Substitute these values and the coordinates of the given point (-1, -4) into the reflection formula to find the image of the point in the line.

Step-by-step explanation:

Hope it helps. G'day mate :)