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.
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Answer 1

To find the equations of the lines based on their intersecting points, we will use the two-point form of the equation of a line.

**Line A:**
The points are (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 the point-slope form of the equation \( y - y_1 = m(x - x_1) \), using (0, 7):
\[
y - 7 = -3(x - 0) \\
y - 7 = -3x \\
y = -3x + 7
\]

Thus, the equation for Line A is:
\[
y = -3x + 7
\]

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**Line B:**
The points are (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 the point-slope form of the equation \( y - y_1 = m(x - x_1) \), using (0, 0):
\[
y - 0 = \frac{7}{3}(x - 0) \\
y = \frac{7}{3}x
\]

Thus, the equation for Line B is:
\[
y = \frac{7}{3}x
\]

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

You would need to drag these equations to their respective boxes based on the lines shown in the graphs.