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.

y = 3 over 7 x
y =-3 over 7 x
y= 7 over 3 x
y = - 7over 3 x
y = 3x
y = -3x
y = 7x
y = -7x
y = 3x + 7
y = -3x + 7
y = 7x +3
y = -7x + 3

Answer 1

To determine the correct equations for each line from the given points, we can use the slope formula and point-slope form of a line:

1. **Finding the equation for Line A using points (0, 7) and (2, 1)**:
- The slope (m) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1) = (0, 7)\) and \((x_2, y_2) = (2, 1)\).
- Plugging in the values:
\[
m = \frac{1 - 7}{2 - 0} = \frac{-6}{2} = -3
\]
- Using the point \( (0, 7) \) (y-intercept form):
The equation is:
\[
y = -3x + 7
\]

2. **Finding the equation for Line B using points (0, 0) and (3, 7)**:
- The slope is calculated using the same formula:
\[
m = \frac{7 - 0}{3 - 0} = \frac{7}{3}
\]
- Using the point \( (0, 0) \) (which is also the y-intercept):
The equation is:
\[
y = \frac{7}{3}x
\]

### Summary of the Equations:
- **Line A**: \(y = -3x + 7\) (from points (0, 7) and (2, 1))
- **Line B**: \(y = \frac{7}{3}x\) (from points (0, 0) and (3, 7))

### Dragged Equations:
- For Line A, drag: **y = -3x + 7**
- For Line B, drag: **y = 7 over 3 x** (which can be represented as **y = \frac{7}{3}x**)