To solve this problem, we need to find the equation of a line that is parallel to the given line [tex]\( 2x + 5y = -34 \)[/tex] and passes through the point [tex]\((-7, -5)\)[/tex].
### Step-by-Step Solution:
1. Identify the coefficients of the original line:
The given line is in the form [tex]\(Ax + By = C\)[/tex], where [tex]\(A = 2\)[/tex], [tex]\(B = 5\)[/tex], and [tex]\(C = -34\)[/tex].
2. Understand the properties of parallel lines:
Parallel lines have the same coefficients for [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. Thus, if we want to find a parallel line to [tex]\(2x + 5y = -34\)[/tex], the coefficients [tex]\(A\)[/tex] and [tex]\(B\)[/tex] for the new line will be the same: [tex]\(A = 2\)[/tex] and [tex]\(B = 5\)[/tex].
3. Substitute the point [tex]\((-7,-5)\)[/tex] into the new line equation to find [tex]\(C\)[/tex]:
The general form of the new line will be:
[tex]\[
2x + 5y = C
\][/tex]
Substituting the point [tex]\((-7, -5)\)[/tex] into this equation:
[tex]\[
2(-7) + 5(-5) = C
\][/tex]
This simplifies to:
[tex]\[
-14 - 25 = C
\][/tex]
[tex]\[
C = -39
\][/tex]
Therefore, the equation of the parallel line that passes through the point [tex]\((-7, -5)\)[/tex] is:
[tex]\[
2x + 5y = -39
\][/tex]
So, the values are:
[tex]\[
A = 2, \quad B = 5, \quad C = -39
\][/tex]
