Answer:
To find the value of x for which f is parallel to g, we need to equate their slopes. The slopes of two lines are equal when their corresponding coefficients of x are equal.
Given:
f: 10x + 5
g: 12x - 9
To find the value of x for which f is parallel to g, we equate their coefficients of x:
10x = 12x
Now, we can solve for x:
10x - 12x = 0
-2x = 0
x = 0
Therefore, the value of x for which f is parallel to g is x = 0.
The theorem that justifies this answer is the "Parallel Lines Theorem." According to this theorem, two lines are parallel if and only if their slopes are equal. In this case, since the slopes of f and g are equal (both coefficients of x are equal to 10), the lines are parallel.