What is the system of equations shown in the graph?

Question

(1 point)
Responses

{y=−x+1y=2x+7
enlarged left brace start layout first row y equals negative x plus 1 second row y equals 2 x plus 7 end layout

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

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

{y=3x+2y=4x+3

Answer 1

To determine the system of equations shown in the graph, we need to identify the slopes and y-intercepts of the lines.

1. Identify the slopes and intersections of the lines: Each equation can be interpreted in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

   • First option:

     • \(y = -x + 1\) (slope = -1, y-intercept = 1)
     • \(y = 2x + 7\) (slope = 2, y-intercept = 7)

   • Second option:

     • \(y = 2x - 3\) (slope = 2, y-intercept = -3)
     • \(y = 3x - 4\) (slope = 3, y-intercept = -4)

   • Third option:

     • \(y = 2x + 3\) (slope = 2, y-intercept = 3)
     • \(y = 3x + 4\) (slope = 3, y-intercept = 4)

   • Fourth option:

     • \(y = 3x + 2\) (slope = 3, y-intercept = 2)
     • \(y = 4x + 3\) (slope = 4, y-intercept = 3)

2. Analyzing slopes:

   • Lines with different slopes will intersect at one point.
   • Lines with the same slope will be parallel and will never intersect.

3. Choose the set according to your observations: Without seeing the graph, I cannot determine the answer for you, but the distinct sets of slopes will help you decide. If you can provide details about the slopes or intercepts from the graph, that will help narrow it down!

As a general approach, look at the intersection points of the lines in the graph to identify which set of equations could represent that scenario.