Which graph shows the solution of −3x−y=3 and y=−3x+4?(1 point)

Question

Responses

Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.

Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.

Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.

Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
Image with alt text: Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
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Answer 1

To determine the type of graph that represents the equations \(-3x - y = 3\) and \(y = -3x + 4\), we first need to analyze the equations.

1. Equation 1: \(-3x - y = 3\)

   We can rearrange this equation into slope-intercept form (y = mx + b):

   \[ -y = 3 + 3x \implies y = -3x - 3 \]

   This line has a slope of -3 and a y-intercept of -3.

2. Equation 2: \(y = -3x + 4\)

   This equation is already in slope-intercept form. It has a slope of -3 and a y-intercept of 4.

Now we can compare the slopes and y-intercepts of both lines:

• Both lines have the same slope of -3.
• The first line (\(y = -3x - 3\)) has a y-intercept of -3, whereas the second line (\(y = -3x + 4\)) has a y-intercept of 4.

Since the two lines have the same slope but different y-intercepts, they are parallel.

Thus, the graph that represents the solution of the equations will show two parallel lines.

Conclusion:

The response that describes "Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid" correctly represents the solution to the equations provided.

Answer 2

which option

Answer 3

The correct option based on the analysis is:

"Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid."

This indicates that the two equations represent parallel lines due to having the same slope but different y-intercepts.

Answer 4

no option 1 2 3 or 4

Answer 5

I apologize for the confusion. Based on your description, it sounds like the options you provided correspond to specific choices. Since I don't have visual access to the options labeled 1, 2, 3, or 4, I cannot directly select one for you.

However, based on the analysis, since the lines are parallel, you should choose the option that indicates:

Option 4: "Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid."

This would be the correct choice. If there is anything else you need help with, please let me know!