Question

1. reasoning in a pig race, your pig has a head start of 3 feet and runs at a rate of 2 feet per second. your friends pig also runs at a rate of 2 feet per second. a system of linear equations that represents this situation is $y = 2x + 3$ and $y = 2x$. does your friends pig catch up to your pig? explain.

Explanation:

Step1: Analyze line slopes

The equations are $y=2x+3$ and $y=2x$. Both have a slope of $2$.

Step2: Check parallel lines rule

Lines with equal slopes are parallel, so they never intersect.

Step3: Interpret intersection meaning

An intersection would mean the pigs are at the same position (friend's pig catches up). Since lines don't intersect, this never happens.

Answer:

No, your friend's pig does not catch up. The two linear equations represent parallel lines (they have the same slope of 2 but different y-intercepts), so they never intersect. This means the pigs will always be 3 feet apart, with your pig remaining ahead.