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 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.

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

Answer 1

To determine which graph shows the solution of the equations \(-3x - y = 3\) and \(y = -3x + 4\), let's analyze and graph both equations.

1. Convert the first equation \(-3x - y = 3\) 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 at \(-3\).

2. The second equation is already in slope-intercept form: \[ y = -3x + 4 \] This line also has a slope of \(-3\) but a y-intercept at \(4\).

Both lines have the same slope of \(-3\), indicating that they are parallel. Since they have different y-intercepts (\(-3\) for the first line and \(4\) for the second line), they will never intersect.

Based on this analysis, the correct graph would be:

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

Since the response indicates that two intersecting lines are present, which is not the case, it is incorrect. Therefore, the answer should be the option indicating parallel lines.