Let's solve the equation [tex]\(a = \frac{b_2 - b_1}{h}\)[/tex] for [tex]\(b_1\)[/tex].
Given equation:
[tex]\[
a = \frac{b_2 - b_1}{h}
\][/tex]
Step 1: Eliminate the denominator on the right-hand side by multiplying both sides by [tex]\(h\)[/tex]:
[tex]\[
a \cdot h = \frac{b_2 - b_1}{h} \cdot h
\][/tex]
[tex]\[
a h = b_2 - b_1
\][/tex]
Step 2: Isolate [tex]\(-b_1\)[/tex] by subtracting [tex]\(b_2\)[/tex] from both sides:
[tex]\[
a h - b_2 = b_2 - b_1 - b_2
\][/tex]
[tex]\[
a h - b_2 = -b_1
\][/tex]
Step 3: Multiply both sides of the equation by [tex]\(-1\)[/tex] to solve for [tex]\(b_1\)[/tex]:
[tex]\[
-b_1 \cdot (-1) = (a h - b_2) \cdot (-1)
\][/tex]
[tex]\[
b_1 = -a h + b_2
\][/tex]
Therefore, the correct answer is:
(D) [tex]\(\boxed{b_1 = -h a + b_2}\)[/tex]
