Use the image to answer the question.

Two lines intersect on the coordinate plane. Both axes range from negative 10 to 10 in increments of 1.

Write the system of equations shown in the graph.

(1 point)
Responses

1 {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

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

3 {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

4 {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
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1 answer

To determine the correct system of equations shown in the graph, it's important to identify the slopes and y-intercepts for each line based on where they intersect the axes.

Without the specific visual representation, I’ll analyze the options presented.

The equations are as follows:

  1. \(y = 2x - 1\) and \(y = 4x + 0.75\)
  2. \(y = 2x + 1\) and \(y = 4x - 3\)
  3. \(y = 2x - 1\) and \(y = 4x + 3\)
  4. \(y = -x + 2\) and \(y = 3x + 4\)

To find the right answer, I would analyze each equation for its slope and intercept:

  1. Option 1: The first line has a slope of 2 (rising steeply) and intercepts at -1. The second line has a slope of 4 (rising even steeper) and intercepts at 0.75. The steepness indicates they likely intersect, but we need more information.

  2. Option 2: The first line has a slope of 2 and intercepts at 1. The second line has a slope of 4 and intercepts at -3.

  3. Option 3: The first line as in option 1 and the second line has a slope of 4 and intercepts at 3.

  4. Option 4: The first line has a negative slope (-1) intersecting at 2. The second line has a positive slope (3) intercepting at 4.

Without the image to refer to, if I had to suggest based on the common characteristics of different graphs:

  • Should there be two lines with a positive intersection and a rising steep gradient, it could likely be either option 1 or 3.
  • If there is variety with a negative slope, option 4 might be possible.

If you can clarify whether the lines are rising or falling, or provide additional key points from the graph, I could narrow it down further.

If you have the image, check for the slopes and y-intercepts of the lines to match the corresponding equations from the options given.