Answer:
-4
Step-by-step explanation:
We are given the equation:-
[tex] \displaystyle \large{x + Cy = \frac{1}{4} }[/tex]
Since we wants to find the value of C that makes the line pass y-intercept which is -1/16.
When we talk about y-intercept, our x-value remains 0 and y-value remains any real number.
It can be expressed as (0,b) point where b is any real numbers.
What we have to do is to substitute (0,-1/16) or x = 0, y = -1/16 in the equation so we can find the value of C.
Thus:-
[tex] \displaystyle \large{x + Cy = \frac{1}{4} } \\ \displaystyle \large{0 + C( - \frac{1}{16} ) = \frac{1}{4} } \\ \displaystyle \large{ - \frac{ C}{16} = \frac{1}{4} }[/tex]
Multiply both sides by GCF.
[tex] \displaystyle \large{ - \frac{ C}{16} = \frac{1}{4} } \\ \displaystyle \large{ - \frac{ C}{16} (16)= \frac{1}{4} (16)} \\ \displaystyle \large{ - C= 4 } \\ \displaystyle \large{ C= - 4 }[/tex]
Therefore, C = -4
