Find the y-intercept of:a ( 2) 72y x= − − b ( 7) 32y x= − − c ( 1) 42y x= + +d ( 3) 2y x= − − e ( 2) 42y x= − +

To find the y-intercepts of the given equations, we need to first understand that the y-intercept occurs where $x = 0$. This means we'll substitute $x = 0$ into each equation and solve for $y$.

Break Down the Problem

1. Substitute $x = 0$ into each equation:
   a. $72y - 2 = 0$
   b. $32y - 7 = 0$
   c. $42y + 1 = 0$
   d. $2y - 3 = 0$
   e. $42y - 2 = 0$

Relevant Concepts

To find the y-intercept, we rewrite each equation in the form $y = mx + b$, where $b$ is the y-intercept. Alternatively, we just need to isolate $y$ after substitution.

Analysis and Detail

1. Find $y$ for each equation:

   1. Equation a: $72y - 2 = 0 \implies 72y = 2 \implies y = \frac{2}{72} = \frac{1}{36}$

   2. Equation b: $32y - 7 = 0 \implies 32y = 7 \implies y = \frac{7}{32}$

   3. Equation c: $42y + 1 = 0 \implies 42y = -1 \implies y = -\frac{1}{42}$

   4. Equation d: $2y - 3 = 0 \implies 2y = 3 \implies y = \frac{3}{2}$

   5. Equation e: $42y - 2 = 0 \implies 42y = 2 \implies y = \frac{2}{42} = \frac{1}{21}$

Verify and Summarize

We calculated the y-intercepts for all equations.

• For Equation a: $y = \frac{1}{36}$
• For Equation b: $y = \frac{7}{32}$
• For Equation c: $y = -\frac{1}{42}$
• For Equation d: $y = \frac{3}{2}$
• For Equation e: $y = \frac{1}{21}$

Final Answer

The y-intercepts are:
a. $\frac{1}{36}$
b. $\frac{7}{32}$
c. $-\frac{1}{42}$
d. $\frac{3}{2}$
e. $\frac{1}{21}$