Use the image to answer the question.

Question

Two lines are shown. The first one is solid and passes through (0, 0) and (1, 5). The second one is dotted and passes through (1, 5) and (0, 3).

What is the system of equations shown in the graph?

Answer 1

To determine the system of equations represented by the lines described:

1. First line (solid line):

   • Passes through the points (0, 0) and (1, 5).
   • The slope \( m \) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{1 - 0} = 5. \]
   • Using the slope-intercept form of the equation \( y = mx + b \), we can plug in the slope and the y-intercept (which is 0 since it passes through (0, 0)): \[ y = 5x. \]

2. Second line (dotted line):

   • Passes through the points (1, 5) and (0, 3).
   • Calculate the slope \( m \): \[ m = \frac{5 - 3}{1 - 0} = 2. \]
   • Using the slope-intercept form:
     • The y-intercept (when \( x = 0 \)) is 3, so: \[ y = 2x + 3. \]

Now, we can write the system of equations for the two lines:

\[ \begin{aligned}

1. & \quad y = 5x \
2. & \quad y = 2x + 3 \end{aligned} \]

This is the system of equations represented by the graph of the two lines.