line has a slope of 0 and passes through the point (3, -5). Which of the following equations represents the line? 


Question 28 Answer

a.

x - 5y = -3 


b.

3x - 5y = -5


c.

y +5 = 0


d.

x+5 = 0

A line with a slope of \(0\) is a **horizontal line**, which means it has the same \(y\)-value for all \(x\)-values along the line. Since the line passes through the point \((3, -5)\), the \(y\)-value for every point on this line must be \(-5\).

Thus, the equation of the line is:
\[
y = -5
\]

The correct choice is **(c) \( y + 5 = 0 \)**, which simplifies to \( y = -5 \).

### Summary:
The correct answer is:
- **(c) \( y + 5 = 0 \)**

Would you like further details on this concept or have any questions?

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Here are some related questions to explore further:
1. What is the general equation of a line with a slope of \(0\)?
2. How do you find the equation of a vertical line passing through a point?
3. How would the equation change if the slope were undefined?
4. What would the equation be if the slope were \(1\) instead?
5. How do you convert a point-slope form equation into slope-intercept form?

**Tip:** Horizontal lines always have equations of the form \( y = \text{constant} \), where the constant is the \( y \)-coordinate of any point on the line.

A line has a slope of 0 and passes through the point (3, -5). Which of the following equations represents the line?

a.

x - 5y = -3

b.

3x - 5y = -5

c.

y + 5 = 0

d.

x + 5 = 0

Discover how to find the equation of a line with a slope of 0 passing through the point (3, -5). This problem involves key algebraic concepts, such as identifying horizontal lines and understanding slope-intercept form, suitable for students in Grades 6-8.

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