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.

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)