Question

The graphs of two lines are shown.

Graph 1 titled 'Line A' has the intersecting points at (0, 7) and (2, 1). Graph 2 titled 'Line B' has the intersecting points at (0, 0) and (3, 7).

Drag the correct equation for each line to the appropriate box.

A. y = 3/7x
B. y = -3/7x
C. y = 7/3x
D. y = -7/3x
E. y = 3x
F. y = -3x
G. y = 7x
H. y = -7x
I. y = 3x + 7
J. y = -3x + 7
K. y = 7x + 3
L. y = -7x +3

Answer 1

To determine the equations of the two lines based on the given points, we will first find the slopes and then form the equations using the point-slope form of a line.

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

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

2. **Use the point-slope form** \(y - y_1 = m(x - x_1)\) with point (0, 7):
\[
y - 7 = -3(x - 0) \implies y = -3x + 7
\]

So, the equation for Line A is **J. y = -3x + 7**.

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

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

2. **Use the point-slope form** with point (0, 0):
\[
y - 0 = \frac{7}{3}(x - 0) \implies y = \frac{7}{3}x
\]

So, the equation for Line B is **C. y = \frac{7}{3}x**.

### Summary:

- Line A: **J. y = -3x + 7**
- Line B: **C. y = \frac{7}{3}x**