To determine which graph shows the solution to the equations \(-3x - y = 3\) and \(y = -3x + 4\), we should first rewrite the first equation in slope-intercept form (y = mx + b) for easier comparison.
Starting with the first equation:
\[ -3x - y = 3 \]
We can isolate \(y\):
\[ -y = 3 + 3x \]
Multiplying both sides by -1 gives:
\[ y = -3x - 3 \]
Now we have two equations in slope-intercept form:
- \(y = -3x - 3\)
- \(y = -3x + 4\)
Both lines have the same slope of -3, which indicates they are parallel lines. Since they have different y-intercepts (-3 and 4), they will never intersect.
From the options you provided, the correct choice would be:
Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
This indicates that they do not intersect and confirms their relationship as parallel lines.
1 answer