The graphs of two lines are shown.

Question

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.