Question: Solve the equation for y.
A.y equals StartFraction 2 x plus 7 Over 17 EndFraction
y equals StartFraction 2 x plus 7 Over 17 EndFraction
B.y equals StartFraction 2 x minus 7 Over 17 EndFraction
y equals StartFraction 2 x minus 7 Over 17 EndFraction
C.y equals StartFraction 2 x minus 17 Over 7 EndFraction
y equals StartFraction 2 x minus 17 Over 7 EndFraction
D.y equals StartFraction 2 x plus 17 Over 7 EndFraction
y equals StartFraction 2 x plus 17 Over 7 EndFraction
1. **State the problem:** Solve the equation for $y$ given the options.
2. **Given equation:** We need to find $y$ in terms of $x$ from the equation implied by the options, which is likely $2x - 7y = 17$ (based on the options).
3. **Isolate $y$:**
$$2x - 7y = 17$$
Subtract $2x$ from both sides:
$$-7y = 17 - 2x$$
4. **Divide both sides by $-7$ to solve for $y$:**
$$y = \frac{17 - 2x}{-7}$$
Show cancellation:
$$y = \frac{\cancel{-7} \times \frac{17 - 2x}{\cancel{-7}}}{} = \frac{17 - 2x}{-7}$$
5. **Simplify the fraction:**
$$y = -\frac{17 - 2x}{7} = \frac{-17 + 2x}{7} = \frac{2x - 17}{7}$$
6. **Final answer:**
$$y = \frac{2x - 17}{7}$$
This corresponds to option C.