Use the image to answer the question.

Question

Two lines intersect on the coordinate plane. Both axes range from negative 10 to 10 in increments of 1.
there are five dots, three on the dotted line, two on the solid (one is on both the solid and dotted)
the points on the dotted lines are 0,3 and -0.75,0, and the one on both lines is -2,-5. the other one on the solid line is 0,-1
Write the system of equations shown in the graph.

(1 point)
Responses

{y=2x−1y=4x+3
enlarged left brace start layout first row y equals 2 x minus 1 second row y equals 4 x plus 3 end layout

{y=2x−1y=4x+0.75
enlarged left brace start layout first row y equals 2 x minus 1 second row y equals 4 x plus 0.75 end layout

{y=−x+2y=3x+4
enlarged left brace start layout first row y equals negative x plus 2 second row y equals 3 x plus 4 end layout

{y=2x+1y=4x−3

Answer 1

To write the system of equations based on the given points, first, we need to find the equations of the two lines described.

1. Dotted Line: The points given on the dotted line are (0, 3) and (-0.75, 0).

   • Using the points, we can determine the slope (m) of the line: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{-0.75 - 0} = \frac{-3}{-0.75} = 4 \]
   • Using the point-slope form (y - y1 = m(x - x1)) with the point (0, 3): \[ y - 3 = 4(x - 0) \implies y = 4x + 3 \]

2. Solid Line: The points on the solid line are (-2, -5) and (0, -1).

   • Again, calculate the slope: \[ m = \frac{-1 - (-5)}{0 - (-2)} = \frac{4}{2} = 2 \]
   • Using the point-slope form with the point (0, -1): \[ y + 1 = 2(x - 0) \implies y = 2x - 1 \]

Thus, the system of equations based on the lines is: \[ \begin{cases} y = 2x - 1 \ y = 4x + 3 \end{cases} \]

Accordingly, the correct response is: \[ {y = 2x - 1 \ y = 4x + 3} \]