Which graph shows the solution of −3x−y=3

Question

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 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.

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

To determine which graph shows the solution to the equations \(-3x - y = 3\) and \(y = -3x + 4\), we can analyze the two lines represented by the equations.

1. Convert \(-3x - y = 3\) to slope-intercept form (y = mx + b): \[ -y = 3 + 3x \implies y = -3x - 3 \] So, the first line has a slope of \(-3\) and a y-intercept of \(-3\).

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

Since both lines have the same slope of \(-3\) but different y-intercepts, they are parallel lines and will never intersect.

Given that the lines are parallel, the correct response would be "Two parallel lines are graphed across a coordinate plane."