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

y=3/7x
y = 3x
y= 3x + 7
y = -3/7 x
y= 7/3x
y = -7/3x
y = -3 x
y = 7x
y = - 7x
y = -3x + 7
y = 7x + 3
y =-7x + 3

Answer 1

To find the correct equations for Line A and Line B, we start by determining their slopes and y-intercepts from the given points.

**Line A: Intersecting points at (0, 7) and (2, 1)**

1. The y-intercept (b) is the value of y when x = 0. From the point (0, 7), we have:
- \( b = 7 \)

2. To find the slope (m), we can use the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 7}{2 - 0} = \frac{-6}{2} = -3
\]

3. Now we can write the equation of Line A in slope-intercept form \( y = mx + b \):
\[
y = -3x + 7
\]

**Line B: Intersecting points at (0, 0) and (3, 7)**

1. The y-intercept (b) is again when x = 0. From the point (0, 0), we have:
- \( b = 0 \)

2. To find the slope (m):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 0}{3 - 0} = \frac{7}{3}
\]

3. Therefore, the equation of Line B in slope-intercept form is:
\[
y = \frac{7}{3}x
\]

Now we can match the found equations:

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

Thus the correct drag-and-drop would be:

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