Question

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

Answer 1

To determine the correct graph for the equations \( -3x - y = 3 \) and \( y = -3x + 4 \), we first need to convert the first equation into the slope-intercept form (y = mx + b).

1. Start with the equation:
\[
-3x - y = 3
\]

2. Rearrange it:
\[
-y = 3 + 3x
\]
\[
y = -3x - 3
\]

Now we have both equations:
- \( y = -3x - 3 \) (from the first equation)
- \( y = -3x + 4 \) (from the second equation)

Next, we can analyze the slopes of both lines:
- The slope of the first line \((-3x - 3)\) is \(-3\).
- The slope of the second line \((-3x + 4)\) is also \(-3\).

Since both lines have the same slope, they are parallel and will never intersect.

Therefore, the correct response would be: **Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.**