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.

A. y = 3/7x
B. y = -3/7x
C. y = 7/3x
D. y = -7/3x
E. y = 3x
F. y = -3x
G. y = 7x
H. y = -7x
I. y = 3x + 7
J. y = -3x + 7
K. y = 7x + 3
L. y = -7x +3

Answer 1

To determine the equations of the two lines based on the given points, we will first find the slopes and then form the equations using the point-slope form of a line.

Line A: Points (0, 7) and (2, 1)

1. Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 7}{2 - 0} = \frac{-6}{2} = -3 \]

2. Use the point-slope form \(y - y_1 = m(x - x_1)\) with point (0, 7): \[ y - 7 = -3(x - 0) \implies y = -3x + 7 \]

So, the equation for Line A is J. y = -3x + 7.

Line B: Points (0, 0) and (3, 7)

1. Calculate the slope (m): \[ m = \frac{7 - 0}{3 - 0} = \frac{7}{3} \]

2. Use the point-slope form with point (0, 0): \[ y - 0 = \frac{7}{3}(x - 0) \implies y = \frac{7}{3}x \]

So, the equation for Line B is C. y = \frac{7}{3}x.

Summary:

• Line A: J. y = -3x + 7
• Line B: C. y = \frac{7}{3}x