To find out what kind of line is represented by the equation $2y = x + 5$, we first rewrite it in slope-intercept form ($y = mx + b$), where $m$ is the slope and $b$ is the y-intercept.

Step 1: Simplify the equation

Start by dividing both sides by 2: $y = \frac{1}{2}x + \frac{5}{2}$

This is now in slope-intercept form.

• Slope (m): $\frac{1}{2}$
• Y-intercept (b): $\frac{5}{2}$ (or 2.5)

Interpretation:

• Slope: Since the slope is positive ($\frac{1}{2}$), the line rises as it moves from left to right.
• Y-intercept: The line crosses the y-axis at $y = \frac{5}{2}$.

Conclusion:

The equation $2y = x + 5$ represents a straight line with a moderate upward slope. It is neither vertical nor horizontal but slightly inclined upwards.

Would you like more details or have any questions?

Here are five related questions:

1. How do you find the x-intercept of a line?
2. What happens if the slope is negative?
3. Can you graph the line using the slope and intercept?
4. How do parallel lines compare in slope?
5. What is the significance of the y-intercept in real-life problems?

Tip: A line’s slope tells you how steep it is—positive slopes go up, negative slopes go down.