Linear Functions and Their Properties

The video tutorial covers linear functions and proportionality, focusing on converting word problems into equations and using T-charts to create equations. It provides examples and homework help to reinforce the concepts, emphasizing the importance of understanding slope and y-intercept in linear equations.

What is the equation of a linear function where the slope is 5 and the y-intercept is 3?

• y = 3x - 5

• y = 5x + 3

• y = 3x + 5

• y = 5x - 3

In a proportional relationship, what is the value of b in the equation y = mx + b?

• b = 1

• b = y

• b = 0

• b = m

If Joe fills a pot at a rate of 8 cups per minute, how long will it take to fill a pot of 64 cups?

• 8 minutes

• 6 minutes

• 10 minutes

• 8.5 minutes

What is the slope of a line if the T-chart shows a change from 0 to 16 dollars over 4 days?

• 4

• 5

• 3

• 2

If you start saving with $0 and save $4 per day, what is the equation representing your savings?

• y = 4x

• y = 4x + 0

• y = x + 4

• y = 0x + 4

How do you find the slope of a line when given two points?

• Subtract the x-values and divide by the y-values

• Subtract the y-values and divide by the x-values

• Add the x-values and y-values

• Multiply the x-values and y-values

If a Pokémon collector starts with 98 Pokémon and collects 13 per week, what is the equation for the total Pokémon collected?

• y = 13x + 98

• y = 98x + 13

• y = 13x - 98

• y = 98x - 13

What is the starting point in a linear function if the T-chart shows 6 gifts at minute 0?

• 3 gifts

• 0 gifts

• 9 gifts

• 6 gifts

If Joey and Chloe wrap gifts at a rate of 3 gifts per minute, how many gifts will they have wrapped after 10 minutes?

• 30 gifts

• 40 gifts

• 20 gifts

• 50 gifts

In a sideways T-chart, what is the first step to find the equation of a linear function?

• Find the midpoint

• Find the x-intercept

• Find the slope

• Find the y-intercept