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.
Image not found

Answer 1

To find the equations of the two lines based on their points of intersection, we can start by calculating the slope-intercept form (y = mx + b) for each line using the given points.

**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. Using the slope and the y-intercept (0, 7), we can 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. Using the slope and the y-intercept (0, 0), we can write the equation:
\[
y = \frac{7}{3}x
\]

**Final equations:**
- Line A: \( y = -3x + 7 \)
- Line B: \( y = \frac{7}{3}x \)

You can drag and place these equations into the correct boxes for Line A and Line B respectively.