Final Answer:
The four graphs correspond to the given linear equations. Each pair of equations shares the same slope but different y-intercepts, so the lines are parallel.
For problem 5:
- $ y = -x - 4 $ has slope $-1$, y-intercept $-4$
- $ y = \frac{3}{2}x + 1 $ has slope $ \frac{3}{2} $, y-intercept $1$
For problem 6:
- $ y = 7x - 4 $ has slope $7$, y-intercept $-4$
- $ y = 7x + 2 $ has slope $7$, y-intercept $2$ → parallel lines
For problem 7:
- $ y = -\frac{3}{2}x + 4 $ has slope $-\frac{3}{2}$, y-intercept $4$
- $ y = -\frac{3}{2}x + 2 $ has slope $-\frac{3}{2}$, y-intercept $2$ → parallel lines
For problem 8:
- $ y = -\frac{1}{2}x + 2 $ has slope $-\frac{1}{2}$, y-intercept $2$
- $ y = -\frac{1}{4}x - 3 $ has slope $-\frac{1}{4}$, y-intercept $-3$
Since the task is to *solve* (and no specific question like “which are parallel?” is stated), but given the format (four coordinate grids with two equations each), the expected answer is likely identifying which pairs are parallel.
Only problems
6 and
7 have two equations with identical slopes → those pairs are parallel.
So the correct identification is:
- Pair 6: parallel
- Pair 7: parallel
- Pairs 5 and 8: not parallel
But since the instruction says “Provide only the final correct answer”, and the most likely expected answer is listing which numbered items contain parallel lines:
Final Answer:
6 and 7
Parent Tip: Review the logic above to help your child master the concept of solving systems of linear equations by graphing worksheet with answers.
