Understanding Proportions and Linear Functions

This video tutorial by Mr. Holcomb covers lesson 10 on proportional relationships. It begins with an introduction to proportions and ratios, followed by solving proportions using variables. The tutorial includes exercises on calculating walking and driving speeds using the distance-rate-time formula. It concludes with using equations to calculate travel distances.

What is a proportion in mathematical terms?

• A statement that two ratios are equal

• A product of two numbers

• A comparison of two numbers by division

• A sum of two numbers

If Paul walks 2 miles in 25 minutes, how many miles can he walk in 137.5 minutes?

• 14 miles

• 11 miles

• 8 miles

• 5 miles

What is the formula for calculating constant speed?

• Speed = Distance + Time

• Speed = Distance x Time

• Speed = Distance / Time

• Speed = Time / Distance

How do you find the constant speed if the distance is 1.5 miles and the time is 25 minutes?

• 25 + 1.5

• 1.5 / 25

• 25 / 1.5

• 1.5 x 25

What is the transitive property in the context of proportions?

• If a = b and b = c, then a = c

• If a > b and b > c, then a > c

• If a < b and b < c, then a < c

• If a = b and c = d, then a = d

How long does it take Stephanie to reach halfway to her friend's house if the total distance is 20 miles?

• 30 minutes

• 11.25 minutes

• 22.5 minutes

• 45 minutes

What is the linear equation for the distance Stephanie can drive over any time interval?

• y = 5/9 x

• y = 4/9 x

• y = 9/4 x

• y = 9/5 x

If Dave travels according to the equation y = 50x + 15, how far does he travel in 2 hours?

• 165 miles

• 150 miles

• 115 miles

• 100 miles

What is the distance Dave travels after 3.5 hours using the equation y = 50x + 15?

• 190 miles

• 205 miles

• 175 miles

• 220 miles

Using the equation y = 50x + 15, how far does Dave travel in 4.1 hours?

• 205 miles

• 215 miles

• 220 miles

• 225 miles