In this aptitude (simplification and analytic geometry) question, you must find the y intercept of a line. For the linear equation 59x + 14y - 112 = 0, set x = 0 and determine the corresponding value of y, which is the y intercept of the line on the coordinate plane.

Introduction / Context:
This question combines basic algebra with coordinate geometry. The goal is to find the y intercept of a straight line given in standard form. The y intercept is the point where the line crosses the y axis, and it is an essential concept in slope intercept representation and in graph sketching for linear functions.

Given Data / Assumptions:
The line is given by the equation 59x + 14y - 112 = 0.
The y intercept is defined as the value of y when x equals 0.
We work in the usual Cartesian coordinate system with x and y real valued.

Concept / Approach:
To find the y intercept of any line, we set x = 0 in the equation and solve for y. This is because any point on the y axis has x coordinate equal to zero. The resulting value gives the vertical coordinate at which the line meets the y axis. The process requires simple substitution and solution of a linear equation in one variable.

Step-by-Step Solution:
Start from the equation 59x + 14y - 112 = 0. Set x = 0 to represent a point on the y axis. Substitute: 59 * 0 + 14y - 112 = 0, which simplifies to 14y - 112 = 0. Add 112 to both sides: 14y = 112. Divide by 14: y = 112 / 14 = 8. So the y intercept is 8, and the point is (0, 8).

Verification / Alternative check:
We can also rearrange the equation into slope intercept form y = mx + c. Starting from 59x + 14y - 112 = 0, move terms: 14y = -59x + 112. Divide by 14 to get y = (-59/14)x + 112/14. The constant term 112/14 simplifies to 8. In y = mx + c form, c is the y intercept, so again we obtain y intercept equal to 8, which confirms the result.

Why Other Options Are Wrong:
Option -8 would arise if a sign mistake is made when moving 112 across the equals sign. Option 14 results from incorrectly dividing or ignoring the coefficient of y. Option 28 and 59 are unrelated to the derived intercept because they correspond to other coefficients in the equation rather than the constant term divided by the coefficient of y. Only the value 8 satisfies the definition of the y intercept for this line.

Common Pitfalls:
Students often forget to set x exactly to zero or mishandle the algebraic rearrangement, especially with signs. Another pitfall is to confuse the slope with the intercept or to read off numbers incorrectly from the original equation. Writing the intermediate step 14y - 112 = 0 clearly and then solving carefully helps avoid these issues.

Final Answer:
The y intercept of the line 59x + 14y - 112 = 0 is 8.