What is the system of equations shown in the graph?

Question

(1 point)
Responses

{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=−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=3x+2y=4x+3

Answer 1

To determine the correct system of equations from the graph, we need to identify the equations of the lines represented in the graph. Unfortunately, you haven't provided the graph here, but I can guide you on how to analyze it:

1. Identify the slopes and y-intercepts: Look at where each line crosses the y-axis (the y-intercept) and assess the angle of inclination to determine the slope.
2. Examine the points of intersection: If the graph displays where the lines intersect, locate those points to help identify the equations.
3. Match the numbers: Compare your findings with the given options to see which pair of equations corresponds with the lines in the graph.

If you are able to analyze the graph using these steps, you can confidently choose the correct system of equations. If you describe the graph or provide any specific details (like intercepts or slopes), I can help you determine the correct answer!

Answer 2

it only gives (-1, 1) and (2, 7)

Answer 3

Given the points \((-1, 1)\) and \((2, 7)\), we can use these points to create two equations for the lines represented in the graph.

Finding the slope of the line between the points:

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

Finding the equation of the line:

Now that we have the slope \(m = 2\), we can use the point-slope form of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] Using point \((-1, 1)\): \[ y - 1 = 2(x + 1) \] Simplifying this gives: \[ y - 1 = 2x + 2 \implies y = 2x + 3 \]

Finding the second equation if required:

Since the problem indicates a system of equations, we might be looking for two intersecting lines. We don't have a second pair of points given, but let's analyze the options:

If we assume the second line must also intersect at the same points, we can try determining a parallel line or a different line.

Possible Candidate Lines:

Now we will evaluate the possible equations you've provided with the line we derived:

1. {y = 2x - 3, y = 3x - 4}: Different slopes; does not intersect at the provided points.
2. {y = 2x + 3, y = 3x + 4}: The first equation matches directly; the second one has a different slope.
3. {y = -x + 1, y = 2x + 7}: Different slopes; does not match.
4. {y = 3x + 2, y = 4x + 3}: Different slopes; does not match.

Conclusion

From the derived line, \(y = 2x + 3\) matches only the option \({y = 2x + 3, y = 3x + 4}\), which suggests the second line might have a certain slope.

To finalize: The answer is {y = 2x + 3, y = 3x + 4}.

If you find the second equation, you can verify its intersection with \(y = 2x + 3\) at the points provided.