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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.
Line A: Line B:

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

1 answer

To determine the equations of the lines based on the given points, we need to find the slope (m) and y-intercept (b) for each line.

For Line A:

  1. The given points are (0, 7) and (2, 1).
  2. Calculate the slope m using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 7}{2 - 0} = \frac{-6}{2} = -3 \]
  3. The y-intercept (b) from the point (0, 7) is 7.
  4. The equation of Line A in slope-intercept form (y = mx + b) is: \[ y = -3x + 7 \]

For Line B:

  1. The given points are (0, 0) and (3, 7).
  2. Calculate the slope m using the same formula: \[ m = \frac{7 - 0}{3 - 0} = \frac{7}{3} \]
  3. The y-intercept (b) from the point (0, 0) is 0.
  4. The equation of Line B is: \[ y = \frac{7}{3}x \]

Final Answers:

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

Response Placement:

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