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

Question

Responses

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.

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 represents the solution to the equations \(-3x - y = 3\) and \(y = -3x + 4\), we need to analyze both equations.

1. First equation (\(-3x - y = 3\)):

   • We can rearrange it into slope-intercept form (\(y = mx + b\)): \[ -y = 3 + 3x \] \[ y = -3x - 3 \] So, the first line has a slope of -3 and a y-intercept of -3.

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

   • This is already in slope-intercept form, where the slope is -3 and the y-intercept is 4.

Now we observe that both lines have the same slope (-3), which means they are parallel. The difference in y-intercepts (-3 and 4) confirms that they will never intersect.

Based on this analysis, the correct graph must show two parallel lines. Therefore, the response that indicates "Two parallel lines are graphed across a coordinate plane" is the correct answer.