Question

Point 1 on line A: (0, 7)
Point 2 on line A: (2, 1)

Point 1 on line B: (0, 0)
Point 2 on line B: (3, 7)

What equation would fit line A and line B?

Answer 1

To find the equations of lines A and B, we can use the slope-intercept form of a line, which is given by the equation:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept.

### Line A
**Points**: (0, 7) and (2, 1)

1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 7}{2 - 0} = \frac{-6}{2} = -3
\]

2. **Use one point to find the intercept (b)**:
We can use point (0, 7) since it's already in the y-intercept form:
- When \( x = 0 \), \( y = 7 \), so \( b = 7 \).

3. **Write the equation**:
\[
y = -3x + 7
\]

### Line B
**Points**: (0, 0) and (3, 7)

1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 0}{3 - 0} = \frac{7}{3}
\]

2. **Use one point to find the intercept (b)**:
Using point (0, 0):
- When \( x = 0 \), \( y = 0 \), so \( b = 0 \).

3. **Write the equation**:
\[
y = \frac{7}{3}x
\]

### Summary of Equations
- **Equation of line A**: \( y = -3x + 7 \)
- **Equation of line B**: \( y = \frac{7}{3}x \)