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

Question

Responses

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

2: 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.

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

4: Two intersecting lines are graphed across a coordinate plane

Answer 1

To determine which graph corresponds to the equations \( -3x - y = 3 \) and \( y = -3x + 4 \), we can analyze the equations.

1. Rearranging the first equation \( -3x - y = 3 \) gives us: \[ y = -3x - 3 \]

2. The second equation is already given as \( y = -3x + 4 \).

Now, both equations can be written in slope-intercept form \( y = mx + b \):

• For \( y = -3x - 3 \), the slope \( m \) is \(-3\) and the y-intercept \( b \) is \(-3\).
• For \( y = -3x + 4 \), the slope \( m \) is also \(-3\) but the y-intercept \( b \) is \(4\).

Since both lines have the same slope (-3), they are parallel. Therefore, the correct response is:

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