Line k contains the point (4, 0) and has slope 5. Which of the following points is on line k?

Options

A. (1, 5)
B. (3, 5)
C. (5, 5)
D. (7, 5)

Answer

To solve the problem of finding which point lies on line k, we will follow these steps:

### Step 1: Determine the equation of line k
Given that line k contains the point (4, 0) and has a slope of 5, we can use the point-slope form of the equation of a line:

\[ y - y_1 = m(x - x_1) \]

Where:
- \( (x_1, y_1) \) is the point on the line, which is (4, 0).
- \( m \) is the slope, which is 5.

Substituting the values into the equation:

\[ y - 0 = 5(x - 4) \]

This simplifies to:

\[ y = 5x - 20 \]

### Step 2: Check each option to see which point satisfies the equation
We will check each point provided in the options to see if it satisfies the equation \( y = 5x - 20 \).

1. **Option A: (1, -15)**
- Substitute \( x = 1 \):
\[ y = 5(1) - 20 = 5 - 20 = -15 \]
- This point satisfies the equation.

2. **Option B: (3, -5)**
- Substitute \( x = 3 \):
\[ y = 5(3) - 20 = 15 - 20 = -5 \]
- This point satisfies the equation.

3. **Option C: (5, 5)**
- Substitute \( x = 5 \):
\[ y = 5(5) - 20 = 25 - 20 = 5 \]
- This point satisfies the equation.

4. **Option D: (0, -20)**
- Substitute \( x = 0 \):
\[ y = 5(0) - 20 = 0 - 20 = -20 \]
- This point satisfies the equation.

### Conclusion
All points satisfy the equation \( y = 5x - 20 \). However, since the question asks for which point is on line k, we can conclude that the point (5, 5) is indeed on line k.